## news

##### Undergraduate Prizes and Awards 2021-2022

Congratulations to this year’s prize and award recipients! Thomas Temple Hoopes Prize From the estate of Thomas T. Hoopes, Class of 1919, Harvard received a...

##### Mark Kisin Elected to American Academy of Arts and Sciences

We are thrilled to announce that Perkins Professor of Mathematics and Director of Graduate Studies Mark Kisin is among sixteen Harvard faculty elected to the...

##### Demystifying Math 55

By Anastasia Yefremova Few undergraduate level classes have the distinction of nation-wide recognition that Harvard University’s Math 55 has. Officially comprised of Mathematics 55A “Studies...

##### Math Question Center helps undergraduates with PSets

If you're a Harvard University student taking an entry-level math course and you haven't heard of the Math Question Center (MQC) yet, you could be...

See Older News

## announcements

##### **New Dates: June 15-17, 2022**: THE CIRCLE AT INFINITY: AN INTERNATIONAL COLLOQUIUM IN HONOR OF CURTIS T. MCMULLEN
June 15, 2022 - June 17, 2022
New Dates: June 15-17, 2022 Conference Poster Confirmed speakers: Serge Cantat, Université de Rennes I Danny Calegari, University of Chicago Laura DeMarco, Harvard...
##### Advances in Mathematical Physics: A Conference in Honor of Elliott H. Lieb on his 90th Birthday.
July 30, 2022 - August 1, 2022
Advances in Mathematical Physics A Conference in Honor of Elliott H. Lieb on his 90th Birthday Dates: July 30-August 1, 2022 Harvard University July 30...
See Older Announcements

## upcoming events

• June 6, 2022 - June 8, 2022
2022 Symposium on Foundations of Responsible Computing (FORC)

CMSA EVENT

• June 15, 2022 - June 17, 2022
Science Center Hall C

ANNOUNCEMENTS, CONFERENCE

• June 21, 2022 - June 24, 2022
CMSA, 20 Garden St, G10

CMSA EVENT

< 2022 >
April
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1
• SEMINARS

##### SEMINARSCMSA General Relativity Program: The nonlinear stability of the Schwarzschild family of black holes

All day
April 1, 2022-April 1, 2022

I will present aspects of a theorem, joint with Mihalis Dafermos, Gustav Holzegel and Igor Rodnianski, on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.

March 29 – April 1, 2022: 10:00am – 12:00pm ET, each day

Location: Hybrid. CMSA main seminar room, G-10. Zoom link will be available.

All in-person attendees must register online.

• SEMINARS

##### SEMINARSSpecial Talks by Harvard MATH Concentrators: Computational algebraic geometry and the Hilbert scheme

10:00 AM-10:25 AM
April 1, 2022
1 Oxford Street, Cambridge, MA 02138 USA

Raluca Vlad, will speak on Computational algebraic geometry and the Hilbert scheme

• SEMINARS

##### SEMINARSSpecial Talks by Harvard MATH Concentrators: Lurie’s construction of Lubin-Tate spectra

10:30 AM-10:55 AM
April 1, 2022
1 Oxford Street, Cambridge, MA 02138 USA

Tristan Yang, will speak on Lurie’s construction of Lubin-Tate spectra

• SEMINARS

##### SEMINARSSpecial Talk: (A)History of Shapes

2:00 PM-2:45 PM
April 1, 2022
1 Oxford Street, Cambridge, MA 02138 USA

Dylan Wilson will speak on (A)History of Shapes

• SEMINARS

##### SEMINARSSpecial Talk: From unique factorization to the shapes of spaces

3:15 PM-4:00 PM
April 1, 2022
1 Oxford Street, Cambridge, MA 02138 USA

Melanie Wood will speak on From unique factorization to the shapes of spaces

2
3
4
• SEMINARS

##### SEMINARSCMSA General Relativity Program Conference

All day
April 4, 2022-April 8, 2022

Monday, April 4, 2022

Tuesday, April 5, 2022

Wednesday, April 6, 2022

Thursday, April 7, 2022

Friday, April 8, 2022

For the full schedule, please see: https://cmsa.fas.harvard.edu/gr-program/

This conference will be held virtually on Zoom. Registration is required.
Webinar Registration

A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• CMSA EVENT: CMSA General Relativity Conference

##### CMSA EVENTCMSA General Relativity Conference

9:30 AM-5:00 PM
April 4, 2022-April 8, 2022

The Harvard CMSA will be hosting a conference on General Relativity from April 4-8, 2022.
This conference will be held virtually on Zoom. Registration is required.
Webinar Registration A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• CMSA EVENT: 2022 Yip Lecture: Extraterrestrial Life

##### CMSA EVENT2022 Yip Lecture: Extraterrestrial Life

7:00 PM-8:00 PM
April 4, 2022
1 Oxford Street, Cambridge MA, 02139

Are we alone? It would be arrogant to think that we are, given that a quarter of all stars host a habitable Earth-size planet. Upcoming searches will aim to detect markers of life in the atmospheres of planets outside the Solar System. We also have unprecedented technologies to detect signs of intelligent civilizations through industrial pollution of planetary atmospheres, space archaeology of debris from dead civilizations or artifacts such as photovoltaic cells that are used to re-distribute light and heat on the surface of a planet or giant megastructures. Our own civilization is starting to explore interstellar travel. Essential information may also arrive as a “message in a bottle”, implying that we should examine carefully any unusual object that arrives to our vicinity from outside the Solar System, such as `Oumuamua.

Registration is required
In-person option: Harvard Science Center:  Register Online for in-person
Online option: livestream via Zoom Webinar: Register Online for Zoom

Refreshments will be served between 6:30–7:00 pm before the lecture.

5
• SEMINARS

##### SEMINARSCMSA General Relativity Program Conference

All day
April 5, 2022-April 8, 2022

Monday, April 4, 2022

Tuesday, April 5, 2022

Wednesday, April 6, 2022

Thursday, April 7, 2022

Friday, April 8, 2022

For the full schedule, please see: https://cmsa.fas.harvard.edu/gr-program/

This conference will be held virtually on Zoom. Registration is required.
Webinar Registration

A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• SEMINARS

##### SEMINARSMath Picture Language Seminar: Analytic Langlands correspondence for complex curves

9:30 AM-10:30 AM
April 5, 2022

I will start the lecture with a brief introduction to various flavors of the Langlands correspondence. I will then explain the setup of a new flavor: the analytic Langlands correspondence for complex curves which was recently fomulated by Pavel Etingof, David Kazhdan, and myself (see arXiv:1908.09677, 2103.01509, and 2106.0524). It can be interpreted in terms of a quantum integrable system, which is obtained by “doubling” the celebrated quantum Hitchin system.

• CMSA EVENT: CMSA Algebraic Geometry in String Theory: Regularized integrals on Riemann surfaces and correlations functions in 2d chiral CFTs

##### CMSA EVENTCMSA Algebraic Geometry in String Theory: Regularized integrals on Riemann surfaces and correlations functions in 2d chiral CFTs

9:30 AM-10:30 AM
April 5, 2022

I will report a recent approach of regularizing divergent integrals on configuration spaces of Riemann surfaces, introduced by Si Li and myself in arXiv:2008.07503, with an emphasis on genus one cases where modular forms arise naturally. I will then talk about some applications in studying correlation functions in 2d chiral CFTs, holomorphic anomaly equations, etc. If time permits, I will also mention a more algebraic formulation of this notion of regularized integrals in terms of mixed Hodge structures.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• CMSA EVENT: CMSA General Relativity Conference

##### CMSA EVENTCMSA General Relativity Conference

9:30 AM-5:00 PM
April 5, 2022-April 8, 2022

The Harvard CMSA will be hosting a conference on General Relativity from April 4-8, 2022.
This conference will be held virtually on Zoom. Registration is required.
Webinar Registration A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARRegular centralizers and the wonderful compactification

3:00 PM-4:00 PM
April 5, 2022
1 Oxford Street, Cambridge, MA 02138 USA

The universal centralizer of a complex semisimple adjoint group G is the family of regular centralizers in G, parametrized by the regular conjugacy classes. It has a natural symplectic structure which is inherited from the cotangent bundle of G. I will construct a smooth, log-symplectic relative compactification of this family using the wonderful compactification of G. Its compactified centralizer fibers are isomorphic to Hessenberg varieties, and its symplectic leaves are indexed by root system combinatorics. I will also explain how to produce a multiplicative analogue of this construction, by moving from the Poisson to the quasi-Poisson setting.

• SEMINARS

##### SEMINARSJoint Harvard-CUHK-YMSC Differential Geometry Seminar: Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds

9:30 PM-10:30 PM
April 5, 2022

Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.

https://cuhk.zoom.us/j/92433760489

(Meeting ID: 924 3376 0489; Passcode: 20220406)

6
• SEMINARS

##### SEMINARSCMSA General Relativity Program Conference

All day
April 6, 2022-April 8, 2022

Monday, April 4, 2022

Tuesday, April 5, 2022

Wednesday, April 6, 2022

Thursday, April 7, 2022

Friday, April 8, 2022

For the full schedule, please see: https://cmsa.fas.harvard.edu/gr-program/

This conference will be held virtually on Zoom. Registration is required.
Webinar Registration

A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• CMSA EVENT: CMSA General Relativity Conference

##### CMSA EVENTCMSA General Relativity Conference

9:30 AM-5:00 PM
April 6, 2022-April 8, 2022

The Harvard CMSA will be hosting a conference on General Relativity from April 4-8, 2022.
This conference will be held virtually on Zoom. Registration is required.
Webinar Registration A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• CMSA EVENT: CMSA Colloquium: What is Mathematical Consciousness Science?

##### CMSA EVENTCMSA Colloquium: What is Mathematical Consciousness Science?

9:30 AM-10:30 AM
April 6, 2022

In the last three decades, the problem of consciousness – how and why physical systems such as the brain have conscious experiences – has received increasing attention among neuroscientists, psychologists, and philosophers. Recently, a decidedly mathematical perspective has emerged as well, which is now called Mathematical Consciousness Science. In this talk, I will give an introduction and overview of Mathematical Consciousness Science for mathematicians, including a bottom-up introduction to the problem of consciousness and how it is amenable to mathematical tools and methods.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Late time von Neumann entropy and measurement-induced phase transition

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Late time von Neumann entropy and measurement-induced phase transition

10:30 AM-11:30 AM
April 6, 2022

Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• NUMBER THEORY SEMINAR

##### NUMBER THEORY SEMINARNumber Theory: Isolated points on modular curves

3:00 PM-4:00 PM
April 6, 2022
1 Oxford Street, Cambridge, MA 02138 USA

Let C be an algebraic curve over a number field. Faltings’s theorem on rational points on subvarieties of abelian varieties implies that all algebraic points on C arise in algebraic families, with finitely many exceptions.  These exceptions are known as isolated points. We study how isolated points behave under morphisms and then specialize to the case of modular curves.  We show that isolated points on X_1(n) push down to isolated points on a modular curve whose level is bounded by a constant that depends only on the j-invariant of the isolated point.  This is joint work with A.
Bourdon, O. Ejder, Y. Liu, and F. Odumodu.

• HARVARD-MIT COMBINATORICS SEMINAR

##### HARVARD-MIT COMBINATORICS SEMINARMIT-Harvard-MSR Combinatorics Seminar: Optimal Mixing of Glauber Dynamics for Spin Systems via Spectral Independence

4:15 PM-5:15 PM
April 6, 2022

Consider the Gibbs distribution of the hardcore model over all independent sets of a given graph, where the probability density of each independent set J is proportional to lambda^|J| where lambda is a parameter. We study the single-site update Markov chain known as the Glauber dynamics for generating independent sets from this distribution. In each step, the dynamics picks a vertex uniformly at random and updates its status (inside or outside the independent set) conditional on the status of all other vertices. We prove optimal (nearly linear) mixing time bounds of the Glauber dynamics on bounded-degree graphs when lambda < lambda_c, beyond which it is known the dynamics can be exponentially slow. To establish our
result, we utilize and improve the spectral independence approach of Anari, Liu, and Oveis Gharan (2020) and show optimal mixing time of the Glauber dynamics for spin systems when the maximum eigenvalues of
associated influence matrices are bounded.

• OPEN NEIGHBORHOOD SEMINAR

##### OPEN NEIGHBORHOOD SEMINARThe mathematics of misinformation

4:30 PM-5:30 PM
April 6, 2022
1 Oxford Street, Cambridge, MA 02138 USA

In this talk I’ll gently survey various roles mathematics (often, but not always, in the form of machine learning) plays in our information ecosystem. I’ll discuss the math behind YouTube’s recommendation algorithm and Facebook’s News Feed algorithm and the impact the choice of objective function has on what society sees and thinks. I’ll explain how graph theory is used to quantitatively study the spread of news and misinformation on social media, and also how it is used to detect bot accounts. And I’ll explain the math behind deepfake photos and videos and text generating AI. No prior knowledge of machine learning or data science will be assumed, and the math will be accessible to all undergraduates.

• SEMINARS

##### SEMINARSJoint Harvard-CUHK-YMSC Differential Geometry Seminar: Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds

9:30 PM-10:30 PM
April 6, 2022

Gromov-Witten invariants of holomorphic symplectic 4-folds vanish and one can consider the corresponding reduced theory. In this talk, we will explain a definition of Gopakumar-Vafa type invariants for such a reduced theory. These invariants are conjectured to be integers and have alternative interpretations using sheaf theoretic moduli spaces. Our conjecture is proved for the product of two K3 surfaces, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.

7
• SEMINARS

##### SEMINARSCMSA General Relativity Program Conference

All day
April 7, 2022-April 8, 2022

Monday, April 4, 2022

Tuesday, April 5, 2022

Wednesday, April 6, 2022

Thursday, April 7, 2022

Friday, April 8, 2022

For the full schedule, please see: https://cmsa.fas.harvard.edu/gr-program/

This conference will be held virtually on Zoom. Registration is required.
Webinar Registration

A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• CMSA EVENT: CMSA Interdisciplinary Science: The space of vector bundles on spheres: algebra, geometry, topology

##### CMSA EVENTCMSA Interdisciplinary Science: The space of vector bundles on spheres: algebra, geometry, topology

9:00 AM-10:00 AM
April 7, 2022

Bott periodicity relates vector bundles on a topological space X to vector bundles on X “times a sphere”.   I’m not a topologist, so I will try to explain an algebraic or geometric incarnation, in terms of vector bundles on the Riemann sphere.   I will attempt to make the talk introductory, and (for the most part) accessible to those in all fields, at the expense of speaking informally and not getting far.   This relates to recent work of Hannah Larson, as well as joint work with (separately) Larson and Jim Bryan.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• SEMINARS

##### SEMINARSMath Picture Language Seminar: A Natural Limitation for Properly Human Scientific Progress

9:30 AM-10:30 AM
April 7, 2022

It follows rather directly from Gödel that mathematical progress per mathematician should diminish with time. The real problem is what relation there is between human mathematics and the set of consequences of the ZFC axioms.

https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Lattice Gauge Theory View of Toric Codes, X-cube, and More

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Lattice Gauge Theory View of Toric Codes, X-cube, and More

9:30 AM-11:00 AM
April 7, 2022

Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• CMSA EVENT: CMSA General Relativity Conference

##### CMSA EVENTCMSA General Relativity Conference

9:30 AM-5:00 PM
April 7, 2022-April 8, 2022

The Harvard CMSA will be hosting a conference on General Relativity from April 4-8, 2022.
This conference will be held virtually on Zoom. Registration is required.
Webinar Registration A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• SEMINARS

##### SEMINARSAlgebraic Dynamics: Torsion points of elliptic curves via Berkovich spaces over Z

10:00 AM-12:00 PM
April 7, 2022

Berkovich spaces over Z may be seen as fibrations containing complex analytic spaces as well as p-adic analytic spaces, for every prime number p. We will give an introduction to those spaces and explain how they may be used in an arithmetic context to prove height inequalities. As an application, following a strategy by DeMarco-Krieger-Ye, we will give a proof of a conjecture of Bogomolov-Fu-Tschinkel on uniform bounds on the number of common images on P^1 of torsion points of two elliptic curves.

• CMSA EVENT: CMSA Active Matter: Theories of branching morphogenesis

##### CMSA EVENTCMSA Active Matter: Theories of branching morphogenesis

1:00 PM-2:00 PM
April 7, 2022

The morphogenesis of branched tissues has been a subject of long-standing debate. Although much is known about the molecular pathways that control cell fate decisions, it remains unclear how macroscopic features of branched organs, including their size, network topology and spatial pattern are encoded. Based on large-scale reconstructions of the mouse mammary gland and kidney, we begin by showing that statistical features of the developing branched epithelium can be explained quantitatively by a local self-organizing principle based on a branching and annihilating random walk (BARW). In this model, renewing tip-localized progenitors drive a serial process of ductal elongation and stochastic tip bifurcation that terminates when active tips encounter maturing ducts. Then, based on reconstructions of the developing mouse salivary gland, we propose a generalisation of BARW model in which tips arrested through steric interaction with proximate ducts reactivate their branching programme as constraints become alleviated through the expansion of the underlying mesenchyme. This inflationary branching-arresting random walk model offers a more general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the tissue into which it expands.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

8
• SEMINARS

##### SEMINARSCMSA General Relativity Program Conference

All day
April 8, 2022-April 8, 2022

Monday, April 4, 2022

Tuesday, April 5, 2022

Wednesday, April 6, 2022

Thursday, April 7, 2022

Friday, April 8, 2022

For the full schedule, please see: https://cmsa.fas.harvard.edu/gr-program/

This conference will be held virtually on Zoom. Registration is required.
Webinar Registration

A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• CMSA EVENT: CMSA General Relativity Conference

##### CMSA EVENTCMSA General Relativity Conference

9:30 AM-5:00 PM
April 8, 2022-April 8, 2022

The Harvard CMSA will be hosting a conference on General Relativity from April 4-8, 2022.
This conference will be held virtually on Zoom. Registration is required.
Webinar Registration A few talks will be held in hybrid formats, with talks given from the CMSA seminar room, G-10. Advanced registration for in-person components is required.
In-Person Registration

• SEMINARS

##### SEMINARSGauge Theory: 4-manifolds with boundary and fundamental group Z

3:30 PM-4:30 PM
April 8, 2022
1 Oxford Street, Cambridge, MA 02138 USA

In this talk I will discuss work in progress in which we classify topological 4-manifolds with boundary and fundamental group Z, under some mild assumptions on the boundary. We apply this classification to provide an algebraic classification of surfaces in simply-connected 4-manifolds with 3-sphere boundary, where the fundamental group on the surface complement is Z. We also compare these homeomorphism classifications with the smooth setting, showing for example that every Hermitian form over the ring of integer Laurent polynomials arises as the equivariant intersection form of a pair of exotic smooth 4-manifolds with boundary and fundamental group Z. This work is joint with Anthony Conway and Mark Powell.

9
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11
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• CMSA EVENT: CMSA Combinatorics, Physics and Probability Seminar: BCFW recursion relations and non-planar positive geometry

##### CMSA EVENTCMSA Combinatorics, Physics and Probability Seminar: BCFW recursion relations and non-planar positive geometry

9:30 AM-10:30 AM
April 12, 2022
20 Garden Street, Cambridge, MA 02138

There is a close connection between the scattering amplitudes in planar N=4 SYM theory and the cells in the positive Grassmannian. In the context of BCFW recursion relations the tree-level S-matrix is represented as a sum of planar on-shell diagrams (aka plabic graphs) and associated with logarithmic forms on the Grassmannian cells of certain dimensionality. In this talk, we explore non-adjacent BCFW shifts which naturally lead to non-planar on-shell diagrams and new interesting subspaces inside the real Grassmannian.

in person – CMSA, 20 Garden St, Room G10

via Zoom – register at:  CMSA Combinatorics, Physics and Probability Seminar

• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARNormal bundles of canonical curves

3:00 PM-4:00 PM
April 12, 2022

The extrinsic geometry of the canonical model of a nonhyperelliptic curve captures many aspects of the intrinsic geometry of the curve.  In this talk I will discuss joint work with Izzet Coskun and Eric Larson in which we show that the normal bundle of a general canonical curve of genus at least 7 is always semistable.  This makes substantial progress towards a conjecture of Aprodu–Farkas–Ortega, and answers it completely in a third of all cases.

13
• CMSA EVENT: CMSA Colloquium: Quantisation in monoidal categories and quantum operads

##### CMSA EVENTCMSA Colloquium: Quantisation in monoidal categories and quantum operads

9:30 AM-10:30 AM
April 13, 2022

The standard definition of symmetries of a structure given on a set S (in the sense of Bourbaki) is the group of bijective maps S to S, compatible with this structure.
But in fact, symmetries of various structures related to storing and transmitting information (such as information spaces) are naturally embodied in various classes of loops such as Moufang loops, – nonassociative analogs of groups.
The idea of symmetry as a group is closely related to classical physics, in a very definite sense, going back at least to Archimedes. When quantum physics started to replace classical, it turned out that classical symmetries must also be replaced by their quantum versions, e.g. quantum groups.

In this talk we explain how to define and study quantum versions of symmetries, relevant to information theory and other contexts.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• NUMBER THEORY SEMINAR

##### NUMBER THEORY SEMINAREuler systems and the p-adic Langlands correspondence

3:00 PM-4:00 PM
April 13, 2022
1 Oxford Street, Cambridge, MA 02138 USA

About 2 years ago, I have given a new construction of the Euler system of cyclotomic units via Eisenstein congruences in which the p-adic Langlands correspondence for GL_2(\Q_p) plays a central role. In this talk, I want to explain how one can extend this method to obtain a large class of new Euler systems attached to ordinary automorphic forms. This is a work in progress.

• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Late time von Neumann entropy and measurement-induced phase transition

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Late time von Neumann entropy and measurement-induced phase transition

8:30 PM-10:00 PM
April 13, 2022

**Note special time**

It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.

We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
—–

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For information on how to join, please see:  https://cmsa.fas.harvard.edu/quantum-matter-seminar

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• CMSA EVENT: CMSA Interdisciplinary Science Seminar: SIMPLEs: a single-cell RNA sequencing imputation strategy preserving gene modules and cell clusters variation

##### CMSA EVENTCMSA Interdisciplinary Science Seminar: SIMPLEs: a single-cell RNA sequencing imputation strategy preserving gene modules and cell clusters variation

9:00 AM-10:00 AM
April 14, 2022

A main challenge in analyzing single-cell RNA sequencing (scRNA-seq) data is to reduce technical variations yet retain cell heterogeneity. Due to low mRNAs content per cell and molecule losses during the experiment (called ‘dropout’), the gene expression matrix has a substantial amount of zero read counts. Existing imputation methods treat either each cell or each gene as independently and identically distributed, which oversimplifies the gene correlation and cell type structure. We propose a statistical model-based approach, called SIMPLEs (SIngle-cell RNA-seq iMPutation and celL clustErings), which iteratively identifies correlated gene modules and cell clusters and imputes dropouts customized for individual gene module and cell type. Simultaneously, it quantifies the uncertainty of imputation and cell clustering via multiple imputations. In simulations, SIMPLEs performed significantly better than prevailing scRNA-seq imputation methods according to various metrics. By applying SIMPLEs to several real datasets, we discovered gene modules that can further classify subtypes of cells. Our imputations successfully recovered the expression trends of marker genes in stem cell differentiation and can discover putative pathways regulating biological processes.

For information on how to join, please go to: https://cmsa.fas.harvard.edu/interdisciplinary-science-seminar

• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Cancellation of the vacuum energy and Weyl anomaly in the standard model, and a two-sheeted, CPT-symmetric universe

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Cancellation of the vacuum energy and Weyl anomaly in the standard model, and a two-sheeted, CPT-symmetric universe

9:30 AM-11:00 AM
April 14, 2022

I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields.  Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos.  Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).

As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role.  Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times.  Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime.  This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole).  It also makes a number of testable predictions.

(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)

—–

Subscribe to Harvard CMSA Quantum Matter and other seminar videos (more to be uploaded):

Subscribe to Harvard CMSA seminar mailing list: https://forms.gle/1ewa7KeP6BxBuBeRA

For information on how to join, please see:  https://cmsa.fas.harvard.edu/quantum-matter-seminar

• SEMINARS

##### SEMINARSAlgebraic Dynamics: Dynamical cancellation

4:00 PM-6:00 PM
April 14, 2022

Let X be a projective variety and let f be a dominant endomorphism of f, both of which are defined over a number field K. We consider the question of when there is some integer n, depending only on X and K, such that whenever x and y are K-points of X with the property that some iterate of f maps x and y to the same point, we necessarily have that the n-th iterate of f also achieves this.  We consider this an instance of “dynamical cancellation’’ and we show that such a cancellation result holds for etale morphisms of projective varieties as well as self-maps of smooth projective curves.  As a result we are able to prove a general cancellation result for semigroups of polynomials: if f_1, … , f_r are polynomials of degree at least two then there is a proper closed subset of P^1 x P^1 with the property that for any a, b in K satisfying phi(a)=phi(b) for some phi in the semigroup generated by f_1, … f_r under composition, we necessarily have (a,b) lies in this closed subset.  Moreover, we show that this Z can be taken to be the union of the diagonal with a finite set of points for “non-exceptional” semigroups.  This is joint work with Matt Satriano and Yohsuke Matsusawa.

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• CMSA EVENT: Workshop on Machine Learning and Mathematical Conjecture

##### CMSA EVENTWorkshop on Machine Learning and Mathematical Conjecture

9:00 AM-5:00 PM
April 15, 2022
1 Oxford Street, Cambridge, MA 02138 USA

On April 15, 2022, the CMSA will hold a one-day workshop, Machine Learning and Mathematical Conjecture, related to the New Technologies in Mathematics Seminar Series. Organizers: Michael R. Douglas (CMSA/Stony Brook/IAIFI) and Peter Chin (CMSA/BU).

Machine learning has driven many exciting recent scientific advances. It has enabled progress on long-standing challenges such as protein folding, and it has helped mathematicians and mathematical physicists create new conjectures and theorems  in knot theory, algebraic geometry, and representation theory.

At this workshop, we will bring together mathematicians, theoretical physicists and machine learning researchers to review the state of the art in machine learning, discuss how ML results can be used to inspire, test and refine precise conjectures, and identify mathematical questions which may be suitable for this approach.

Speakers:

James Halverson, Northeastern University Dept. of Physics and IAIFI

Fabian Ruehle, Northeastern University Dept. of Physics and Mathematics and IAIFI

Andrew Sutherland, MIT Department of Mathematics

 9:30 am – 10:20 am James Halverson: Machine Learning for Mathematicians 10:30 am – 11:20 am Andrew Sutherland: Number Theory 11:30 am – 12:20 pm Fabian Ruehle: Knot Theory Lunch break 2:00 pm –3:30 pm Computer demonstrations 3:45 pm – 4:45 pm Discussion

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.

For a list of lodging options convenient to the Center, please visit our recommended lodgings page.All non-Harvard affiliated visitors to the CMSA building will need to complete this covid form prior to arrival: https://forms.gle/xKykcNcXq7ciZuvJ8To attend, please REGISTER ONLINE.

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• SEMINARS

##### SEMINARSMathematical Science Literature Lecture: Eric Maskin- Three Introductory Lectures on Game Theory for Mathematicians

9:30 AM-11:00 AM
April 18, 2022

On April 18, 20, and 22, Eric Maskin (Harvard University) will give three introductory lectures on Game Theory.

April 18, 2022 | 9:30–11:00 am ET
Title: Game Theory Basics and Classical Existence Theorems
Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo

April 20, 2022 | 9:30–11:00 am ET
Title: Mechanism Design
Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?

April 22, 2022 | 9:30–11:00 am ET
Title: Auction Theory
Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).

Register online at: https://harvard.zoom.us/webinar/register/WN_yOFpmqM1QCenXQlcpCZOYA

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• CMSA EVENT: CMSA Algebraic Geometry in String Theory: Equivariant Verlinde algebra and quantum K-theory of the moduli space of vortices

##### CMSA EVENTCMSA Algebraic Geometry in String Theory: Equivariant Verlinde algebra and quantum K-theory of the moduli space of vortices

9:30 AM-10:30 AM
April 19, 2022

In studying complex Chern-Simons theory on a Seifert manifold, Gukov-Pei proposed an equivariant Verlinde formula, a one-parameter deformation of the celebrated Verlinde formula. It computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the Hitchin moduli space. Gukov-Pei conjectured that the equivariant Verlinde numbers are equal to the equivariant quantum K-invariants of a non-compact (Kahler) quotient space studied by Hanany-Tong.

In this talk, I will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) Bradlow-Higgs triples. It is based on work in progress with Wei Gu and Du Pei.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• SEMINARS

##### SEMINARSMath Picture Language Seminar: Vertical versus horizontal isoperimetry

9:30 AM-10:30 AM
April 19, 2022

We will explain an isoperimetric-type inequality for subsets of the Heisenberg group that controls the size of the (suitably defined) vertical boundary by the perimeter. This inequality was conceived for a specific application that we will describe, but in the course of its investigation there were twists and turns that unearthed unexpected geometric phenomena and led to further applications to longstanding questions. These will be explained, but the main purpose of this talk is to show the geometric structures that arise in the proof.

https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

• CMSA EVENT: CMSA Combinatorics, Physics and Probability Seminar: Some combinatorics of Wilson loop diagrams

##### CMSA EVENTCMSA Combinatorics, Physics and Probability Seminar: Some combinatorics of Wilson loop diagrams

9:30 AM-10:30 AM
April 19, 2022
1 Oxford Street, Cambridge, MA 02138 USA

Wilson loop diagrams can be used to study amplitudes in N=4 SYM.  I will set them up and talk about some of their combinatorial aspects, such as how many Wilson loop diagrams give the same positroid and how to combinatorially read off the dimension and the denominators for the integrands.

This seminar will be held in person and online via Zoom.

To register for the in person seminar, please see: https://forms.gle/rMHV1fQP6Lu576eH9

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

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• CMSA EVENT: Mathematical Science Literature Lecture: Eric Maskin- Three Introductory Lectures on Game Theory for Mathematicians

##### CMSA EVENTMathematical Science Literature Lecture: Eric Maskin- Three Introductory Lectures on Game Theory for Mathematicians

9:30 AM-11:00 AM
April 20, 2022

On April 18, 20, and 22, Eric Maskin (Harvard University) will give three introductory lectures on Game Theory.

April 18, 2022 | 9:30–11:00 am ET
Title: Game Theory Basics and Classical Existence Theorems
Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo

April 20, 2022 | 9:30–11:00 am ET
Title: Mechanism Design
Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?

April 22, 2022 | 9:30–11:00 am ET
Title: Auction Theory
Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).

Register online at: https://harvard.zoom.us/webinar/register/WN_yOFpmqM1QCenXQlcpCZOYA

• CMSA EVENT: CMSA Strongly Correlated Quantum Materials and High-Temperature Superconductors Series

##### CMSA EVENTCMSA Strongly Correlated Quantum Materials and High-Temperature Superconductors Series

11:30 AM-1:00 PM
April 20, 2022

Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.

https://cmsa.fas.harvard.edu/strongly-correlated-materials/

https://cmsa.fas.harvard.edu/quantum-matter-seminar/

• HARVARD-MIT COMBINATORICS SEMINAR

##### HARVARD-MIT COMBINATORICS SEMINARMIT-Harvard-MSR Combinatorics Seminar: Threshold for Steiner triple systems

4:15 PM-5:15 PM
April 20, 2022

We prove that with high probability $G^{(3)}(n,n^{-1+o(1)})$ contains a  spanning Steiner triple system. We also prove the analogous result for  spanning Latin squares. This threshold is sharp up to a subpolynomial  factor. Our result follows from a novel bootstrapping scheme that utilizes  iterative absorption as well as recent connections which have been  established between thresholds and spread measures. Joint work with Ashwin  Sah and Michael Simkin.

• OPEN NEIGHBORHOOD SEMINAR

##### OPEN NEIGHBORHOOD SEMINAROpen Neighborhood Seminar: Runge’s method for solving diophantine equations

4:30 PM-5:30 PM
April 20, 2022

It has been proved that there is no general algorithm for finding all the integer solutions to a multivariable polynomial equation. Nevertheless, there are some methods that succeed if the equation has a certain form. I will explain one such method. If you want to try to rediscover it yourself, try to provably find all the integer solutions to y^2 = x^4 + 4x^3 – 2x^2 + 6x + 20.

*This week the seminar will be held at the Science Center North Lawn

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• CMSA EVENT: CMSA Interdisciplinary Science Seminar: Secure Multi-Party Computation: from Theory to Practice

##### CMSA EVENTCMSA Interdisciplinary Science Seminar: Secure Multi-Party Computation: from Theory to Practice

9:00 AM-10:00 AM
April 21, 2022

Encryption is the backbone of cybersecurity. While encryption can secure data both in transit and at rest, in the new era of ubiquitous computing, modern cryptography also aims to protect data during computation. Secure multi-party computation (MPC) is a powerful technology to tackle this problem, which enables distrustful parties to jointly perform computation over their private data without revealing their data to each other. Although it is theoretically feasible and provably secure, the adoption of MPC in real industry is still very much limited as of today, the biggest obstacle of which boils down to its efficiency.

My research goal is to bridge the gap between the theoretical feasibility and practical efficiency of MPC. Towards this goal, my research spans both theoretical and applied cryptography. In theory, I develop new techniques for achieving general MPC with the optimal complexity, bringing theory closer to practice. In practice, I design tailored MPC to achieve the best concrete efficiency for specific real-world applications. In this talk, I will discuss the challenges in both directions and how to overcome these challenges using cryptographic approaches. I will also show strong connections between theory and practice.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• CMSA EVENT: CMSA Interdisciplinary Science Seminar: Scalable and Provably Robust Algorithms for Machine Learning

##### CMSA EVENTCMSA Interdisciplinary Science Seminar: Scalable and Provably Robust Algorithms for Machine Learning

9:00 AM-10:00 AM
April 21, 2022

Abstract: As machine learning plays a more prominent role in our society, we need learning algorithms that are reliable and robust.  It is important to understand whether existing algorithms are robust against adversarial attacks and design new robust solutions that work under weaker assumptions.  The long-term goal is to bridge the gap between the growing need for robust algorithms and the lack of systematic understanding of robustness.

In this talk, I will discuss the challenges that arise in the design and analysis of robust algorithms for machine learning.  I will focus on three lines of my recent work: (1) designing faster and simpler algorithms for high-dimensional robust statistics where a small fraction of the input data is arbitrarily corrupted, (2) analyzing the optimization landscape of non-convex approaches for low-rank matrix problems and making non-convex optimization robust against semi-random adversaries, and (3) considering learning in the presence of strategic behavior where the goal is to design good algorithms that account for the agents’ strategic responses.

Bio: Yu Cheng is an assistant professor in the Mathematics department at the University of Illinois at Chicago.  He obtained his Ph.D. in Computer Science from the University of Southern California.  Before joining UIC, he was a postdoc at Duke University and a visiting member at the Institute for Advanced Study.  His main research interests include machine learning, optimization, and game theory.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

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• CMSA EVENT: Mathematical Science Literature Lecture: Eric Maskin- Three Introductory Lectures on Game Theory for Mathematicians

##### CMSA EVENTMathematical Science Literature Lecture: Eric Maskin- Three Introductory Lectures on Game Theory for Mathematicians

9:30 AM-11:00 AM
April 22, 2022

On April 18, 20, and 22, Eric Maskin (Harvard University) will give three introductory lectures on Game Theory.

April 18, 2022 | 9:30–11:00 am ET
Title: Game Theory Basics and Classical Existence Theorems
Abstract: Games in extensive and normal form. Equilibrium existence theorems by Nash, von Neumann, and Zermelo

April 20, 2022 | 9:30–11:00 am ET
Title: Mechanism Design
Abstract: Given a social goal, under what circumstances can we design a game to achieve that goal?

April 22, 2022 | 9:30–11:00 am ET
Title: Auction Theory
Abstract: Equivalences among four standard auctions: the high-bid auction (the high bidder wins and pays her bid); the second-bid auction (the high bidder wins and pays the second-highest bid); the Dutch auction (the auctioneer lowers the price successively until some bidder is willing to pay); and the English auction (bidders raise their bids successively until no one wants to bid higher).

Register online at: https://harvard.zoom.us/webinar/register/WN_yOFpmqM1QCenXQlcpCZOYA

• HARVARD-MIT COMBINATORICS SEMINAR

##### HARVARD-MIT COMBINATORICS SEMINARMIT-Harvard-MSR Combinatorics Seminar: A Type B analog of the Whitehouse representations

3:30 PM-4:30 PM
April 22, 2022

The Eulerian idempotents of the symmetric group generate a family of  representations—the Eulerian representations—that have connections to  configuration spaces, equivariant cohomology, and Solomon’s descent  algebra. These representations are defined in terms of S_n, but can be  “lifted” to representations of S_{n+1} called the Whitehouse  representations. I will describe this story in detail and present recent  work generalizing it to the hyperoctahedral group (e.g. Type B). In this  setting, configuration spaces will be replaced by certain orbit  configuration spaces and Solomon’s descent algebra is replaced by the  Mantaci-Reutenauer algebra. All of the above will be defined in the talk,  which is based on the preprint https://arxiv.org/abs/2203.09504.

• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Higgs = SPT

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Higgs = SPT

3:30 PM-5:00 PM
April 22, 2022

The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

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• CMSA EVENT: CMSA Combinatorics, Physics and Probability Seminar: Algebraic Statistics with a View towards Physics

##### CMSA EVENTCMSA Combinatorics, Physics and Probability Seminar: Algebraic Statistics with a View towards Physics

9:00 AM-10:00 AM
April 26, 2022
1 Oxford Street, Cambridge, MA 02138 USA

We discuss the algebraic geometry of maximum likelihood estimation from the perspective of scattering amplitudes in particle physics. A guiding examples the moduli space of n-pointed rational curves. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions to rational function equations. Their number is an Euler characteristic. Soft limit degenerations are combined with certified numerical methods for concrete computations.

This seminar will be held in person and online via Zoom.

To register for the in person seminar, please see: https://forms.gle/rMHV1fQP6Lu576eH9

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• CMSA EVENT: CMSA Algebraic Geometry in String Theory: Modularity of mirror families of log Calabi–Yau surfaces

##### CMSA EVENTCMSA Algebraic Geometry in String Theory: Modularity of mirror families of log Calabi–Yau surfaces

9:30 AM-10:30 AM
April 26, 2022

In ‘Mirror symmetry for log Calabi–Yau surfaces I’, given a smooth log Calabi–Yau surface pair (Y,D), Gross–Hacking–Keel constructed its mirror family as the spectrum of an explicit algebra whose structure coefficients are determined by the enumerative geometry of (Y,D). As a follow-up of the work of Gross–Hacking–Keel, when (Y,D) is positive, we prove the modularity of the mirror family as the universal family of log Calabi-Yau surface pairs deformation equivalent to (Y,D) with at worst du Val singularities. As a corollary, we show that the ring of regular functions of a smooth affine log Calabi–Yau surface has a canonical basis of theta functions. The key step towards the proof of the main theorem is the application of the tropical construction of singular cycles and explicit formulas of period integrals given in the work of Helge–Siebert. This is joint work with Jonathan Lai.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard-MIT Algebraic Geometry Seminar: Generalized crystalline cohomology theories

3:00 PM-4:00 PM
April 26, 2022

For a prime number p, the crystalline cohomology of an F_p-scheme can be regarded as an analogue of the singular cohomology with Z_p coefficients of a topological space. On the topological side, there are other “generalized” cohomology theories, e.g. K-theory and cobordism, and these are related to natural operations on singular cohomology. In this talk, I will discuss analogues of these generalized cohomology theories and cohomology operations in the crystalline setting.

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• CMSA EVENT: CMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

##### CMSA EVENTCMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

All day
April 27, 2022-April 29, 2022

On April 27–29, 2022, the CMSA will host a workshop on Nonlinear Algebra and Combinatorics.

Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard).

In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

All non-Harvard affiliated visitors to the CMSA building are required to complete this covid form prior to arrival: https://forms.gle/xKykcNcXq7ciZuvJ8

Registration is required: Register Online

Speakers:

• Federico Ardila (San Francisco State)
• Nima Arkani-Hamed (IAS)
• Nick Early (Max Planck Institute)
• Chris Eur (Harvard)
• Claudia Fevola (Max Planck Institute)
• Christian Gaetz (Harvard)
• Yuji Kodama (Ohio State University)
• Yelena Mandelshtam (Berkeley)
• Sebastian Mizera (IAS)
• Matteo Parisi (Harvard CMSA)
• Emma Previato (Boston University)
• Anna Seigal (Harvard)
• Melissa Sherman-Bennett (University of Michigan)
• Simon Telen (Max Planck Institute)
• Charles Wang (Harvard)

### Schedule

Wednesday, April 27, 2022

Thursday, April 28, 2022

Friday, April 29, 2022

• CMSA EVENT: CMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

##### CMSA EVENTCMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

9:00 AM-6:00 PM
April 27, 2022-April 29, 2022
1 Oxford Street, Cambridge, MA 02138 USA

In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

Invited speakers include Federico Ardila, Nima Arkani-Hamed, Madeleine Brandt, Freddy Cachazo, Chris Eur, Claudia Fevola, Christian Gaetz, Yuji Kodama, Fatemeh Mohammadi, Matteo Parisi, Anna Seigal, Melissa Sherman-Bennett, Simon Telen, and Charles Wang.

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

• CMSA EVENT: CMSA Colloquium: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

##### CMSA EVENTCMSA Colloquium: Long common subsequences between bit-strings and the zero-rate threshold of deletion-correcting codes

9:30 AM-10:30 AM
April 27, 2022

Suppose we transmit n bits on a noisy channel that deletes some fraction of the bits arbitrarily. What’s the supremum p* of deletion fractions that can be corrected with a binary code of non-vanishing rate? Evidently p* is at most 1/2 as the adversary can delete all occurrences of the minority bit. It was unknown whether this simple upper bound could be improved, or one could in fact correct deletion fractions approaching 1/2.

We show that there exist absolute constants A and delta > 0 such that any subset of n-bit strings of size exp((log n)^A) must contain two strings with a common subsequence of length (1/2+delta)n. This immediately implies that the zero-rate threshold p* of worst-case bit deletions is bounded away from 1/2.

Our techniques include string regularity arguments and a structural lemma that classifies bit-strings by their oscillation patterns. Leveraging these tools, we find in any large code two strings with similar oscillation patterns, which is exploited to find a long common subsequence.

This is joint work with Xiaoyu He and Ray Li.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• NUMBER THEORY SEMINAR

##### NUMBER THEORY SEMINARNumber Theory Seminar: Slopes of modular forms and reductions of crystalline representations

3:00 PM-4:00 PM
April 27, 2022
1 Oxford Street, Cambridge, MA 02138 USA

The ghost conjecture predicts slopes of modular forms whose residual representation is locally reducible.  In this talk, we’ll examine locally irreducible representations and discuss recent progress on formulating a conjecture in this case.  It’s a lot trickier and the story remains incomplete, but we will discuss how an irregular ghost conjecture is intimately related to reductions of crystalline representations.

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• CMSA EVENT: CMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

##### CMSA EVENTCMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

All day
April 28, 2022-April 29, 2022

On April 27–29, 2022, the CMSA will host a workshop on Nonlinear Algebra and Combinatorics.

Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard).

In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

All non-Harvard affiliated visitors to the CMSA building are required to complete this covid form prior to arrival: https://forms.gle/xKykcNcXq7ciZuvJ8

Registration is required: Register Online

Speakers:

• Federico Ardila (San Francisco State)
• Nima Arkani-Hamed (IAS)
• Nick Early (Max Planck Institute)
• Chris Eur (Harvard)
• Claudia Fevola (Max Planck Institute)
• Christian Gaetz (Harvard)
• Yuji Kodama (Ohio State University)
• Yelena Mandelshtam (Berkeley)
• Sebastian Mizera (IAS)
• Matteo Parisi (Harvard CMSA)
• Emma Previato (Boston University)
• Anna Seigal (Harvard)
• Melissa Sherman-Bennett (University of Michigan)
• Simon Telen (Max Planck Institute)
• Charles Wang (Harvard)

### Schedule

Wednesday, April 27, 2022

Thursday, April 28, 2022

Friday, April 29, 2022

• CMSA EVENT: CMSA Interdisciplinary Science Seminar: Intersection number and systole on hyperbolic surfaces

##### CMSA EVENTCMSA Interdisciplinary Science Seminar: Intersection number and systole on hyperbolic surfaces

9:00 AM-10:00 AM
April 28, 2022

Let X be a compact hyperbolic surface. We can see that there is a constant C(X) such that the intersection number of the closed geodesics is  \leq C(X) times the product of their lengths. Consider the optimum constant C(X). In this talk, we describe its asymptotic behavior in terms of systole,  length of the shortest closed geodesic on X.

For information on how to join, please go to: https://cmsa.fas.harvard.edu/interdisciplinary-science-seminar

• CMSA EVENT: CMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

##### CMSA EVENTCMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

9:00 AM-6:00 PM
April 28, 2022-April 29, 2022
1 Oxford Street, Cambridge, MA 02138 USA

In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

Invited speakers include Federico Ardila, Nima Arkani-Hamed, Madeleine Brandt, Freddy Cachazo, Chris Eur, Claudia Fevola, Christian Gaetz, Yuji Kodama, Fatemeh Mohammadi, Matteo Parisi, Anna Seigal, Melissa Sherman-Bennett, Simon Telen, and Charles Wang.

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Aspects of 4d supersymmetric dynamics and geometry

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Aspects of 4d supersymmetric dynamics and geometry

10:30 AM-12:00 PM
April 28, 2022

We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/seminars-and-colloquium/

• CMSA EVENT: CMSA Active Matter Seminar: Building active nematic and active polar liquids out of biological machines

##### CMSA EVENTCMSA Active Matter Seminar: Building active nematic and active polar liquids out of biological machines

1:00 PM-2:00 PM
April 28, 2022

Active matter describes out-of-equilibrium materials composed of motile building blocks that convert free energy into mechanical work. The continuous input of energy at the particle scale liberates these systems from the constraints of thermodynamic equilibrium, leading to emergent collective behaviors not found in passive materials. In this talk, I will describe our recent efforts to build simple active systems composed of purified proteins and identify generic emergent behaviors in active systems. I will first discuss two distinct activity-driven instabilities in suspensions of microtubules and molecular motors. Second, I will describe a new model system for polar fluid whose collective dynamics are driven by the non-equilibrium turnover of actin filaments. Our results illustrate how biomimetic materials can serve as a platform for studying non-equilibrium statistical mechanics, as well as shine light on the physical mechanisms that regulate self-organization in living matter.

29
• CMSA EVENT: CMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

##### CMSA EVENTCMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

All day
April 29, 2022-April 29, 2022

On April 27–29, 2022, the CMSA will host a workshop on Nonlinear Algebra and Combinatorics.

Organizers: Bernd Sturmfels (MPI Leipzig) and Lauren Williams (Harvard).

In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. For a list of lodging options convenient to the Center, please visit our recommended lodgings page.

All non-Harvard affiliated visitors to the CMSA building are required to complete this covid form prior to arrival: https://forms.gle/xKykcNcXq7ciZuvJ8

Registration is required: Register Online

Speakers:

• Federico Ardila (San Francisco State)
• Nima Arkani-Hamed (IAS)
• Nick Early (Max Planck Institute)
• Chris Eur (Harvard)
• Claudia Fevola (Max Planck Institute)
• Christian Gaetz (Harvard)
• Yuji Kodama (Ohio State University)
• Yelena Mandelshtam (Berkeley)
• Sebastian Mizera (IAS)
• Matteo Parisi (Harvard CMSA)
• Emma Previato (Boston University)
• Anna Seigal (Harvard)
• Melissa Sherman-Bennett (University of Michigan)
• Simon Telen (Max Planck Institute)
• Charles Wang (Harvard)

### Schedule

Wednesday, April 27, 2022

Thursday, April 28, 2022

Friday, April 29, 2022

• GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

##### GAUGE-TOPOLOGY-SYMPLECTIC SEMINARCMSA Workshop on Nonlinear Algebra and Combinatorics from Physics

9:00 AM-6:00 PM
April 29, 2022-April 29, 2022
1 Oxford Street, Cambridge, MA 02138 USA

In recent years, ideas from integrable systems and scattering amplitudes have led to advances in nonlinear algebra and combinatorics. In this short workshop, aimed at younger participants in the field, we will explore some of the interactions between the above topics.

Invited speakers include Federico Ardila, Nima Arkani-Hamed, Madeleine Brandt, Freddy Cachazo, Chris Eur, Claudia Fevola, Christian Gaetz, Yuji Kodama, Fatemeh Mohammadi, Matteo Parisi, Anna Seigal, Melissa Sherman-Bennett, Simon Telen, and Charles Wang.

The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA

• GAUGE-TOPOLOGY-SYMPLECTIC SEMINAR

##### GAUGE-TOPOLOGY-SYMPLECTIC SEMINARPeg Problems: *Cancelled*

3:30 PM-4:30 PM
April 29, 2022
1 Oxford Street, Cambridge, MA 02138 USA

This event has been cancelled for today, April 29, 2022.

I will talk about joint work with Andrew Lobb related to Toeplitz’s square peg problem, which asks whether every (continuous) Jordan curve in the Euclidean plane contains the vertices of a square. Specifically, we show that every smooth Jordan curve contains the vertices of a cyclic quadrilateral of any similarity class. I will describe the context for the result and its proof, which involves symplectic geometry in a surprising way.

This seminar was rescheduled from April 15, 2022**