## news

##### Melanie Matchett Wood Recipient of 2022 MacArthur Fellowship

Earlier today, the John D. and Catherine T. MacArthur Foundation announced the 2022 MacArthur Fellows, recipients of the so-called “genius grant.” The Fellowship—including a generous...

See Older News

## upcoming events

• November 28, 2022 - December 1, 2022
Workshop on Representation Theory, Calabi-Yau Manifolds, and Mirror Symmetry

CMSA EVENT

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• CMSA EVENT: CMSA Active Matter: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk

##### CMSA EVENTCMSA Active Matter: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk

Speaker: Josef Käs – Leipzig University

1:00 PM-2:00 PM
September 6, 2022

Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.
Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.
We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.

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

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• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids

Speaker: Zhengyan Darius Shi – MIT

9:00 AM-10:30 AM
September 7, 2022

Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity   (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result $\sigma(mega) \sim mega^{-2(z-2)/z}$  due to Kim et al. is incorrect for inversion-odd order parameters.

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

• SEMINARS: Informal Seminar: Exotic homeomorphisms and flows (after Sullivan and Freedman)

##### SEMINARSInformal Seminar: Exotic homeomorphisms and flows (after Sullivan and Freedman)

Speaker: Curtis McMullen – Harvard

4:00 PM-5:00 PM
September 7, 2022
1 Oxford Street, Cambridge, MA 02138 USA

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• CMSA EVENT: Diving Into Math with Emmy Noether

##### CMSA EVENTDiving Into Math with Emmy Noether

4:30 PM-6:30 PM
September 10, 2022

Diving Into Math with Emmy Noether

A theatre performance about the life of one of history’s most influential mathematicians.

When: Saturday, September 10, 2022

Panel Discussion: 4:30 p.m. – 5 p.m. | Play: 5:15 p.m. | Reception: 6:30 p.m. – 7:30 p.m.

Where: Harvard University Hilles Cinema, Student Organization Center at Hilles (SOCH)

59 Shepard Street, Cambridge, MA 02138

Panelists:

• Melissa Franklin | Harvard University Mallinckrodt Professor of Physics
• Barry Mazur | Harvard University Gerhard Gade University Professor
• Monica Noether | Vice President, Charles River Associates | Grandniece of Emmy Noether
• David Rowe | Mainz University Professor

Unfortunately, as of right now venue capacity has been reached. If you’d like to sign up to be waitlisted, please register below and we will inform you by Friday, September 9 if seats become available.

#### Waitlist Registration

Emmy Noether (1882-1935) was one of the most influential mathematicians of the last century. Her works and teachings left a lasting mark on modern algebra, opening new avenues for a modern structural perspective in mathematics.

The ensemble Portraittheater Vienna (Austria) together with the Frei Universität Berlin (Germany) produced a biographical play about Emmy Noether, directed by Sandra Schüddekopf and starring Anita Zieher as Emmy. In September 2022, “Diving into Math with Emmy Noether” will tour the USA for the first time and play at several universities and colleges. The Harvard Department of Mathematics and the Center of Mathematical Sciences and Applications (CMSA) are proud to bring this performance to Harvard University.

Based on historical documents and other sources, the script was written by Sandra Schüddekopf and Anita Zieher in cooperation with the historians Mechthild Koreuber and David E. Rowe. On stage and in videos, Emmy Noether’s fascinating personality comes alive in her reflections and conversations with other leading mathematicians of her day. The original play in German has been performed with great success at several universities in Germany and in the Theater Drachengasse in Vienna.

A coproduction by portraittheater Vienna and Freie Universität Berlin. Scientific Board: Mechthild Koreuber, David Rowe.

View the “Diving into Math with Emmy Noether” trailer.

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• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Non-invertible Symmetries in Nature

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Non-invertible Symmetries in Nature

Speaker: Yichul Choi – SUNY Stony Brook

9:30 AM-11:00 AM
September 13, 2022

In this talk, I will discuss non-invertible symmetries in familiar 3+1d quantum field theories describing our Nature. In massless QED, the classical U(1) axial symmetry is not completely broken by the ABJ anomaly. Instead, it turns into a discrete, non-invertible symmetry. The non-invertible symmetry operator is obtained by dressing the naïve U(1) axial symmetry operator with a fractional quantum Hall state. We also find a similar non-invertible symmetry in the massless limit of QCD, which provides an alternative explanation for the neutral pion decay. In the latter part of the talk, I will discuss non-invertible time-reversal symmetries in 3+1d gauge theories. In particular, I will show that in free Maxwell theory, there exists a non-invertible time-reversal symmetry at every rational value of the theta angle.

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

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

• CMSA EVENT: Harvard/MIT Algebraic Geometry Seminar: Dynamical moduli spaces of linear maps with marked points

##### CMSA EVENTHarvard/MIT Algebraic Geometry Seminar: Dynamical moduli spaces of linear maps with marked points

Speaker: Max Weinreich –

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

Moduli spaces of degree d dynamical systems on projective space are fundamental in algebraic dynamics. When the degree d is at least 2, these moduli spaces can be defined via geometric invariant theory (GIT), but when d = 1, there are no GIT stable linear maps. Inspired by the case of genus 0 curves, we show how to recover a nice moduli space by including marked points. Linear maps are the simplest dynamical systems, but with marked points, the moduli space becomes quite subtle. We construct the moduli space of linear maps with marked points, prove its rationality, and show that GIT stability is characterized by subtle dynamical conditions on the marked map related to Hessenberg varieties. The proof is a combinatorial analysis of polytopes generated by root vectors of the A_N lattice from Lie theory.

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• COLLOQUIUMS: CMSA Colloquium: Strategyproof-Exposing Mechanisms Descriptions

##### COLLOQUIUMSCMSA Colloquium: Strategyproof-Exposing Mechanisms Descriptions

Speaker: Yannai Gonczarowski – Harvard

12:00 PM-1:00 PM
September 14, 2022
1 Oxford Street, Cambridge, MA 02138 USA

One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms, it is “strategy-proof”: participants can never gain by misreporting their preferences (say, over schools) to the algorithm. Alas, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds, but rather resort to an appeal to authority: Nobel laureates have proven this property, so one should listen to them. Unsurprisingly perhaps, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it,” which results in a suboptimal match for themselves and for others.

By developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel, starkly different, yet equivalent, description for the Deferred Acceptance algorithm, which, in a precise sense, makes its strategyproofness far more apparent. Our description does have a downside, though: some other of its most fundamental properties—for instance, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop, we mathematically address the question of whether and to what extent this downside is unavoidable, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed, it seems that in the design of all traditional descriptions of the algorithm, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm, at the expense of properties that are mostly of interest to policy makers, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp, which we also support with behavioral experiments in the lab.

Joint work with Ori Heffetz and Clayton Thomas.

• CMSA EVENT: CMSA New Technologies in Mathematics: Breaking the one-mind-barrier in mathematics using formal verification

##### CMSA EVENTCMSA New Technologies in Mathematics: Breaking the one-mind-barrier in mathematics using formal verification

Speaker: Johan Commelin – Mathematisches Institut, Albert-Ludwigs-Universität Freiburg

2:00 PM-3:00 PM
September 14, 2022

In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed, formal verification allows a team of mathematicians to collaborate on a project, without one person understanding all parts of the project. At the same time, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier.

I will use the Liquid Tensor Experiment as an example, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces, following up on a challenge by Peter Scholze.

For more information on how to join, please see: https://cmsa.fas.harvard.edu/tech-in-math/

• NUMBER THEORY SEMINAR: Number Theory Seminar: Symplectic Reidemeister torsion and symplectic L-functions

##### NUMBER THEORY SEMINARNumber Theory Seminar: Symplectic Reidemeister torsion and symplectic L-functions

Speaker: Akshay Venkatesh – IAS

3:00 PM-4:00 PM
September 14, 2022
1 Oxford Street, Cambridge, MA 02138 USA

Many of the quantities appearing in the conjecture of Birch and Swinnerton-Dyer look suspiciously like squares. Motivated by this and related examples, we may ask if the central value of an L-function “of symplectic type” admits a preferred square root.

The answer is no: there’s an interesting cohomological obstruction. More formally, in the everywhere unramified situation over a function field, I will describe an explicit cohomological formula for the L-function modulo squares. This is based on a purely topological result about 3-manifolds. If time permits I’ll speculate on generalizations. This is based on joint work with Amina Abdurrahman.

https://people.math.harvard.edu/~sli/hnts/

• SEMINARS: Informal Seminar: Exotic homeomorphisms and flows (after Sullivan and Freedman)

##### SEMINARSInformal Seminar: Exotic homeomorphisms and flows (after Sullivan and Freedman)

Speaker: Curtis McMullen – Harvard University

4:00 PM-5:00 PM
September 14, 2022

This seminar will be held in Science Center 530 at 4:00pm on Wednesday, September 15th.

Please see the seminar page for more details: https://math.harvard.edu/~ctm/sem/.

• OPEN NEIGHBORHOOD SEMINAR: Incompleteness and infinity

##### OPEN NEIGHBORHOOD SEMINARIncompleteness and infinity

Speaker: W. Hugh Woodin – Harvard University

4:30 PM-5:30 PM
September 14, 2022
1 Oxford Street, Cambridge, MA 02138 USA

A natural speculation is that incompleteness is simply a by-product of infinity. Perhaps one can avoid incompleteness by simply restricting our mathematical scope to the finite. Do we lose anything in this move?

The answer I shall argue, is both yes and no. Along the way I will discuss an entirely new approach to the Godel Incompleteness Theorems which has emerged over the last 15 years. I will also introduce some very large finite numbers which arise naturally from finite combinatorics, and indicate how by invoking these large finite numbers, any number theoretic problem of modern interest can be converted to a finitistic statement.

It is unclear which would be more amazing for these problems of modern interest: This conversion does not always produce an equivalent problem, or that this conversion always does.

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• SEMINARS: CMSA General Relativity Seminar: The Gregory-Laflamme instability of black strings revisited

##### SEMINARSCMSA General Relativity Seminar: The Gregory-Laflamme instability of black strings revisited

Speaker: Professor Pau Figueras – Queen Mary University of London

10:30 AM-11:30 AM
September 15, 2022

In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the Gregory-Laflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular, while our results support the picture of the formation of a naked singularity in finite asymptotic time, the process is more complex than previously thought. In addition, we obtain some hints about the nature of the singularity that controls the pinch off of the string.

This seminar will be held in CMSA GR Seminar room and will be broadcast on Zoom.

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/general-relativity/

• SEMINARS: Gauge Theory and Topology Seminar: Surgery formulae in instanton theory

##### SEMINARSGauge Theory and Topology Seminar: Surgery formulae in instanton theory

Speaker: Zhenkun Li – Stanford

3:00 PM-4:00 PM
September 15, 2022
1 Oxford Street, Cambridge MA, 02139

Instanton homology was first introduced by Floer in 1980s. It has many important applications in the study of 3-manifolds and knots, especially in studying the SU(2) representations of fundamental groups. It is conjectured by Kronheimer and Mrowka that the framed instanton Floer homology of a 3-manifold is isomorphic to the hat version of Heegaard Floer homology, but not much is known beyond families of computational examples. In this talk, I will present some surgery formulae in instanton theory, which helps us understand the framed instanton Floer homology of Dehn surgeries on knots. These surgery formulae provide some important structural properties for instanton theory and enable us to compute the framed instanton Floer homology of many new families of 3-manifolds that come from Dehn surgeries and splicings. This is a join work with Fan Ye.

• THURSDAY SEMINAR SEMINAR: Thursday Seminar: Mixed characteristic cohomology theories and Topological Hochschild Homology

##### THURSDAY SEMINAR SEMINARThursday Seminar: Mixed characteristic cohomology theories and Topological Hochschild Homology

Speaker: Tomer Schlank –

3:30 PM-5:30 PM
September 15, 2022
1 Oxford Street, Cambridge, MA 02138 USA

No additional detail for this event.

• SEMINARS: Algebraic Dynamics: Core entropy of quadratic polynomials

##### SEMINARSAlgebraic Dynamics: Core entropy of quadratic polynomials

Speaker: Kathryn Lindsey – Boston College

4:00 PM-6:00 PM
September 15, 2022

This will be more of a mini-course than a traditional seminar.  I will provide details about the (core) entropy algorithms for quadratic polynomials from my work with Tiozzo and Wu.

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• SEMINARS: Harvard Math Picture Language Seminar: Determining distributions of groups from their moments

##### SEMINARSHarvard Math Picture Language Seminar: Determining distributions of groups from their moments

Speaker: Melanie Wood – Harvard University

9:30 AM-10:30 AM
September 20, 2022

Just as moments of a distribution of real numbers are a powerful tool that (if they are not too large) determine the distribution uniquely, we can consider certain averages as moments of a distribution of groups (or more general algebraic structures).  We discuss how these moments determine a distribution of groups uniquely, and how that can be applied to find distributions of fundamental groups of random 3-manifolds, fundamental groups of curves over finite fields, and to give conjectures for distributions of important groups arising in number theory such as class groups.

• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Morita theory for non-commutative noetherian schemes

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard–MIT Algebraic Geometry Seminar: Morita theory for non-commutative noetherian schemes

Speaker: Yuriy Drozd – Institute of Mathematics of the National Academy of Sciences of Ukraine

3:00 PM-4:00 PM
September 20, 2022
1 Oxford Street, Cambridge, MA 02138 USA

We prove that the categories of coherent (or, equivalently, of quasi-coherent) sheaves over two noetherian non-commutative schemes X and Y are equivalent if and only if there centers C(X) and C(Y) are isomorphic and there is a local progenerator in the category of coherent sheaves over X whose sheaf of endomorphisms is anti-isomorphic to the inverse image of the structure sheaf of Y under the isomorphism X->Y. To prove it, we combine the classical Morita theorem with the Gabriel’s theory of locally noetherian categories.

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• CMSA EVENT: CMSA Topological Quantum Matter Seminar: Geometric test for topological states of matter

##### CMSA EVENTCMSA Topological Quantum Matter Seminar: Geometric test for topological states of matter

Speaker: Semyon Klevtsov – University of Strasbourg

9:00 AM-10:00 AM
September 21, 2022
1 Oxford Street, Cambridge, MA 02138 USA

We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space.Based on joint work with Dimitri Zvonkine (CNRS, University of Paris-Versaille)

• CMSA EVENT: CMSA Active Matter Seminar: Limit and potential of adaptive immunity

##### CMSA EVENTCMSA Active Matter Seminar: Limit and potential of adaptive immunity

Speaker: Shenshen Wang – UCLA

11:00 AM-12:00 PM
September 21, 2022
1 Oxford Street, Cambridge, MA 02138 USA

The adaptive immune system is able to learn from past experiences to better fit an unforeseen future. This is made possible by a diverse and dynamic repertoire of cells expressing unique antigen receptors and capable of rapid Darwinian evolution within an individual. However, naturally occurring immune responses exhibit limits in efficacy, speed and capacity to adapt to novel challenges. In this talk, I will discuss theoretical frameworks we developed to (1) explore functional impacts of non-equilibrium antigen recognition, and (2) identify conditions under which natural selection acting local in time can find adaptable solutions favorable in the long run, through exploiting environmental variations and functional constraints.

This seminar will be held at CMSA, 20 Garden St, seminar room G-10 and on Zoom. For more information on how to join the Zoom, please see: https://cmsa.fas.harvard.edu/event/active-matter-seminar-6/

• CMSA EVENT: CMSA Colloquium: Moduli spaces of graphs

##### CMSA EVENTCMSA Colloquium: Moduli spaces of graphs

Speaker: Melody Chan – Brown

12:30 PM-1:30 PM
September 21, 2022
20 Garden Street, Cambridge, MA 02138

A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs’’ to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.

• CMSA EVENT: CMSA New Technologies in Mathematics Seminar

##### CMSA EVENTCMSA New Technologies in Mathematics Seminar

2:00 PM-3:00 PM
September 21, 2022

• SEMINARS: Informal Seminar: Dynamics: From the circle to Riemann surfaces

##### SEMINARSInformal Seminar: Dynamics: From the circle to Riemann surfaces

Speaker: Curtis McMullen – Harvard

4:00 PM-5:00 PM
September 21, 2022

This seminar will be held in Science Center 530 at 4:00pm on Wednesday, September 21st.

Please see the seminar page for more details: https://math.harvard.edu/~ctm/sem/.

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• SEMINARS: CMSA General Relativity Seminar: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system

##### SEMINARSCMSA General Relativity Seminar: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system

Speaker: Nikolaos Athanasiou –

10:30 AM-11:30 AM
September 22, 2022

Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/event_category/general-relativity/

• SEMINARS: Algebraic Dynamics Seminar: Elephants all the way down: the near-parabolic geometry of the Mandelbrot set

##### SEMINARSAlgebraic Dynamics Seminar: Elephants all the way down: the near-parabolic geometry of the Mandelbrot set

Speaker: Alex Kapiamba – University of Michigan

4:00 PM-6:00 PM
September 22, 2022

Understanding the geometry of The Mandelbrot set, which records dynamical information about every quadratic polynomial, has been a central task in holomorphic dynamics over the past forty years. Near parabolic parameters, the structure of the Mandelbrot set is asymptotically self-similar and resembles a parade of elephants. Near parabolic parameters on these “elephants”, the Mandelbrot set is again self-similar and resembles another parade of elephants. This phenomenon repeats infinitely, and we see different parades of elephants at each scale. In this talk, we will explore the implications of controlling the geometry of these elephants. In particular, we will partially answer Milnor’s conjecture on the optimality of the Yoccoz inequality, and see potential connections to the local connectivity of the Mandelbrot set.

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• SEMINARS: Gauge Theory and Topology Seminar: Instantons mod 2 and indefinite 4-manifolds

##### SEMINARSGauge Theory and Topology Seminar: Instantons mod 2 and indefinite 4-manifolds

Speaker: Mike Miller Eismeier – Columbia

3:30 PM-4:30 PM
September 23, 2022
1 Oxford Street, Cambridge, MA 02138 USA

This talk is on work in preparation with Ali Daemi.

I will explain why Kim Froyshov’s mod 2 instanton invariant q_3 gives information about indefinite 4-manifolds: if H_1(W;Z/2) = 0 and W has boundary Y, then -b^+(W) <= q_3(Y) <= b^-(W). This is the first invariant known to enjoy comparable bounds for indefinite manifolds W.

The key observation is that even when b^+(W) > 0, one can define a Donaldson invariant in the (tilde) instanton homology of boundary(W) — not in the usual instanton tilde complex, but rather a “suspension”. This suspension process accounts for the role of obstructed gluing theory, and does not destroy information about q_3 (but does destroy information about all other types of h-invariant).

As a corollary, we show that there exist integer homology spheres with arbitrary integral surgery number S(Y_n) = n. This answers a question of Dave Auckly. Previously, the state of the art was n=2, and further progress was obstructed by the possibility that the linking matrix be indefinite.

• CMSA EVENT: CMSA/Math Fall Gathering

##### CMSA EVENTCMSA/Math Fall Gathering

4:30 PM-6:00 PM
September 23, 2022

CMSA Fall Gathering will be held on September 23rd from 4:30-6:00pm. All CMSA and Math Affiliates Invited! Hot dogs, popcorn, and hot cider courtesy of Dylan and Pete’s.

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• CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Candidates for Non-Supersymmetric Dualities

##### CMSA EVENTCMSA Quantum Matter in Mathematics and Physics: Candidates for Non-Supersymmetric Dualities

Speaker: Avner Karasik – University Cambridge, UK

9:00 AM-10:30 AM
September 26, 2022

In the talk I will discuss the possibility and the obstructions of finding non-supersymmetric dualities for 4d gauge theories. I will review consistency conditions based on Weingarten inequalities, anomalies and large N, and clarify some subtle points and misconceptions about them. Later I will go over some old and new examples of candidates for non-supersymmetric dualities. The will be based on 2208.07842

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

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• HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry: Cycle-valued quasi-modular forms

##### HARVARD-MIT ALGEBRAIC GEOMETRY SEMINARHarvard-MIT Algebraic Geometry: Cycle-valued quasi-modular forms

Speaker: Francois Greer – Michigan State and MIT

3:00 PM-4:00 PM
September 27, 2022

Arithmetic quotients of Type IV Hermitian symmetric domains have cohomology-valued modular forms whose coefficients are special cycles, by work of Borcherds. These can be interpreted as non-compact period spaces for K3-type Hodge structures. I will describe recent results (joint with P. Engel and S. Tayou) that give mock modular forms whose coefficients are compactified special cycles in a simplicial toroidal compactification. Next, I will discuss an application to the geometry of Severi curves associated to a rational elliptic surface.

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• CMSA EVENT: CMSA Topological Quantum Matter: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow

##### CMSA EVENTCMSA Topological Quantum Matter: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow

Speaker: Ruihua Fan – Harvard University

9:00 AM-10:00 AM
September 28, 2022
1 Oxford Street, Cambridge, MA 02138 USA

One question in the study of topological phases is to identify the topological data from the ground state wavefunction without accessing the Hamiltonian. Since local measurement is not enough, entanglement becomes an indispensable tool. Here, we use modular Hamiltonian (entanglement Hamiltonian) and modular flow to rephrase previous studies on topological entanglement entropy and motivate a natural generalization, which we call the entanglement linear response. We will show how it embraces a previous work by Kim&Shi et al on the chiral central charge, and furthermore, inspires a new formula for the quantum Hall conductance.

• CMSA EVENT: CMSA Colloquium: The Tree Property and uncountable cardinals

##### CMSA EVENTCMSA Colloquium: The Tree Property and uncountable cardinals

Speaker: Dima Sinapova – Rutgers University

12:30 PM-1:30 PM
September 28, 2022
1 Oxford Street, Cambridge, MA 02138 USA

In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes.
We will focus on one such key combinatorial property, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.

• CMSA EVENT: CMSA New Technologies: Statistical mechanics of neural networks: from the geometry of high dimensional error landscapes to beating power law neural scaling

##### CMSA EVENTCMSA New Technologies: Statistical mechanics of neural networks: from the geometry of high dimensional error landscapes to beating power law neural scaling

Speaker: Surya Ganguli – Dept. of Applied Physics, Stanford University

2:00 PM-3:00 PM
September 28, 2022

Statistical mechanics and neural network theory have long enjoyed fruitful interactions.  We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer.  In particular, we will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index.  Second we will review recent work on neural power laws, which reveal that the error of many neural networks falls off as a power law with network size or dataset size.  Such power laws have motivated significant societal investments in large scale model training and data collection efforts.  Inspired by statistical mechanics calculations, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size, sometimes achieving exponential scaling, by collecting small carefully curated datasets rather than large random ones.
References:
Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.
Sorscher, Ben, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022)

This talk will be held on Zoom, for more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/new-technologies-in-mathematics-seminar-series/

• CMSA EVENT: CMSA New Technologies in Mathematics Seminar

##### CMSA EVENTCMSA New Technologies in Mathematics Seminar

Speaker: Surya Ganguli – Department of Applied Physics, Stanford University

2:00 PM-3:00 PM
September 28, 2022

This seminar will be held in person, for more information, please see: https://cmsa.fas.harvard.edu/tech-in-math/

• SEMINARS: Informal Seminar: Introduction to the pentagon: Curves in moduli space

##### SEMINARSInformal Seminar: Introduction to the pentagon: Curves in moduli space

Speaker: Curtis McMullen – Harvard

4:00 PM-5:00 PM
September 28, 2022

This seminar will be held in Science Center 530 at 4:00pm on Wednesday, September 28th.

Please see the seminar page for more details: https://math.harvard.edu/~ctm/sem/.

• OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: From moments to matrices

##### OPEN NEIGHBORHOOD SEMINAROpen Neighborhood Seminar: From moments to matrices

Speaker: John Urschel – Harvard

4:30 PM-5:30 PM
September 28, 2022
1 Oxford Street, Cambridge, MA 02138 USA
Moments of a function give concrete information about the shape of the associated graph and have been thoroughly studied in a wide variety of fields. In this talk, we will discuss a number of classic moment problems and their connection to practical problems in numerical linear algebra.

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• SEMINARS: CMSA General Relativity Seminar: General-relativistic viscous fluids

##### SEMINARSCMSA General Relativity Seminar: General-relativistic viscous fluids

Speaker: Marcelo Disconzi – Vanderbilt University

9:30 AM-10:30 AM
September 29, 2022

The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

For information on how to join, please see:  https://cmsa.fas.harvard.edu/event_category/general-relativity/

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• CMSA EVENT: CMSA Algebraic Geometry in String Theory: GLSM, Homological projective duality and nc resolutions

##### CMSA EVENTCMSA Algebraic Geometry in String Theory: GLSM, Homological projective duality and nc resolutions

Speaker: Mauricio Romo – Tsinghua University

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

Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.

For information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/algebraic-geometry-in-string-theory/

• ANNOUNCEMENTS: Teaching and Teacher Leadership master’s program Info Session

##### ANNOUNCEMENTSTeaching and Teacher Leadership master’s program Info Session

3:00 PM-5:00 PM
September 30, 2022
Teachers change lives – and you can be part of that change by becoming a teacher at the Harvard Graduate School of Education. HGSE’s new Teaching and Teacher Leadership master’s program will prepare you to lead transformative learning experiences that expand opportunity, fuel student success, and make a positive deep impact on young people and their communities. TTL builds on the successes of HGSE’s former teacher education programs, including the Harvard Teacher Fellows, and is committed to welcoming Harvard College undergraduates into meaningful careers in education. The program offers two pathways: a residency model, where you’ll jump into the classroom right away as a teacher of record, and an internship model for those seeking to ramp up teaching responsibility more gradually. TTL is committed to supporting new teachers – with extensive funding to minimize student debt, mentors to learn from, and field experiences that will fuel your professional growth.

Learn more about becoming a math teacher through TTL at our Math Info Session Friday, September 30 at 3pm in SC105. Register here.
• SEMINARS: Gauge Theory and Topology Seminar: Bordered aspects of the Heegaard Floer surgery formulas

##### SEMINARSGauge Theory and Topology Seminar: Bordered aspects of the Heegaard Floer surgery formulas

Speaker: Ian Zemke – Princeton University

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

In this talk, we will discuss bordered aspects of the Heegaard Floer surgery formulas of  Ozsvath–Szabo and Manolescu–Ozsvath. In particular, we will explain how their theories naturally define bordered invariants for manifolds with toroidal boundary components. Time permitting, we will discuss applications of the theory. One application is a proof of the equivalence of lattice homology and Heegaard Floer homology. Another application is a description of the link Floer complexes of algebraic links, which is parallel to Ozsvath and Szabo’s description of the knot Floer complex of an L-space link. The latter application is joint with M. Borodzik and B. Liu.

October