Calendar

On October 4th and October 5th, 2021, Harvard CMSA will host its annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker will be Michael Freedman (Microsoft). The lectures will take place from 11:00am – 12:15pm (ET) on Zoom.

You must register to attend. Register here.

This will be the third annual lecture series held in honor of Raoul Bott.

Lecture 1:

Monday, October 4, 11:00 am – 12:15 pm ET

Title: The Universe from a single Particle

Abstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709 

Lecture 2:

Tuesday, October 5, 11 am – 12:15 pm ET

Title: Controlled Mather Thurston Theorems.

Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374  

The previous Bott Lectures lecture featured Mina Aganagic (UC Berkeley), who spoke on “Two math lessons from string theory.” Information can be found here.

**rescheduled from October 4**

https://harvard.zoom.us/j/977347126
Password: cmsa

In a graph G = (V, E) we consider a system of paths S so that for every two vertices u,v in V there is a unique uv path in S connecting them. The path system is said to be consistent if it is closed under taking subpaths, i.e. if P is a path in S then any subpath of P is also in S. Every positive weight function w: E–>R^+ gives rise to a consistent path system in G by taking the paths in S to be geodesics w.r.t. w. In this case, we say w induces S. We say a graph G is metrizable if every consistent path system in G is induced by some such w.

We’ll discuss the concept of graph metrizability, and, in particular, we’ll see that while metrizability is a rare property, there exists infinitely many 2-connected metrizable graphs.

Joint work with Nati Linial.

Zoom link: https://harvard.zoom.us/j/99715031954?pwd=eVRvbERvUWtOWU9Vc3M2bjN3VndBQT09

Password: 1251442

On October 4th and October 5th, 2021, Harvard CMSA will host its annual Math Science Lectures in Honor of Raoul Bott. This year’s speaker will be Michael Freedman (Microsoft). The lectures will take place from 11:00am – 12:15pm (ET) on Zoom.

You must register to attend. Register here.

This will be the third annual lecture series held in honor of Raoul Bott.

Lecture 1:

Monday, October 4, 11:00 am – 12:15 pm ET

Title: The Universe from a single Particle

Abstract: I will explore a toy model  for our universe in which spontaneous symmetry breaking – acting on the level of operators (not states) – can produce the interacting physics we see about us from the simpler, single particle, quantum mechanics we study as undergraduates. Based on joint work with Modj Shokrian Zini, see arXiv:2011.05917 and arXiv:2108.12709 

Lecture 2:

Tuesday, October 5, 11 am – 12:15 pm ET

Title: Controlled Mather Thurston Theorems.

Abstract: The “c-principle” is a cousin of Gromov’s h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that in certain well-known c-principle contexts only the mildest cobordisms, semi-s-cobordisms, are required. In physical applications, the extra topology (a perfect fundamental group) these cobordisms introduce could easily be hidden in the UV. This leads to a proposal to recast gauge theories such as EM and the standard model in terms of flat connections rather than curvature. See arXiv:2006.00374  

The previous Bott Lectures lecture featured Mina Aganagic (UC Berkeley), who spoke on “Two math lessons from string theory.” Information can be found here.

I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion. For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.

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Subscribe to Harvard CMSA seminar videos (more to be uploaded):
https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww

The infrastructure built to power the Machine Learning revolution has many other uses beyond Deep Learning. Starting from a general architecture-level overview over the lower levels of Google’s TensorFlow machine learning library, we review how this has recently helped us to find all the stable vacua of SO(8) Supergravity in 3+1 dimensions, has allowed major progress on other related questions about M theory, and briefly discuss other applications in field theory and beyond.

https://harvard.zoom.us/j/99651364593?pwd=Q1R0RTMrZ2NZQjg1U1ZOaUYzSE02QT09

Given a prime number l, the elliptic modular polynomial of level l is an explicit equation for the locus of elliptic curves related by an l-isogeny. These polynomials have a large number of algorithmic applications: in particular, they are an essential ingredient in the celebrated SEA algorithm for counting points on elliptic curves over finite fields of large characteristic.

More generally, modular equations describe the locus of isogenous abelian varieties in certain moduli spaces called PEL Shimura varieties. We will present upper bounds on the size of modular equations in terms of their level, and outline a general strategy to compute an isogeny A->A’ given a point (A,A’) where the modular equations are satisfied. This generalizes well-known properties of elliptic modular polynomials to higher dimensions.

The isogeny algorithm is made fully explicit for Jacobians of genus 2 curves. In combination with efficient evaluation methods for modular equations in genus 2 via complex approximations, this gives rise to point counting algorithms for (Jacobians of) genus 2 curves whose
asymptotic costs, under standard heuristics, improve on previous results.

will speak on:

“Angular momentum in general relativity”

Tuesday, October 5, 2021

9:30 – 10:30 AM  *Hong Kong time*

9:30 – 10:30 PM *Eastern Time*

Abstract: The definition of angular momentum in general relativity has been a subtle issue since the 1960′, due to the discovery of “supertranslation ambiguity”: the angular momentums recorded by two distant observers of the same system may not be the same. In this talk, I shall show how the mathematical theory of optimal isometric embedding and quasilocal angular momentum identifies a correction term, and leads to a new definition of angular momentum that is free of any supertranslation ambiguity. This is based on joint work with Po-Ning Chen, Jordan Keller, Ye-Kai Wang, and Shing-Tung Yau.

Zoom Link: https://cuhk.zoom.us/j/93114537124
Meeting ID: 931 1453 7124, Passcode: 20211006

As of 2018, the United States National Institutes of Health estimate that over half a billion people worldwide are affected by autoimmune disorders. Though these conditions are prevalent, treatment options remain relatively poor, relying primarily on various forms of immunosuppression which carry potentially severe side effects and often lose effectiveness overtime. Given this, new forms of therapy are needed. To this end, we have developed methods for the creation of small-interfering RNA (siRNA) for hypervariable regions of the T-cell receptor β-chain gene (TCRb) as a highly targeted, novel means of therapy for the treatment of autoimmune disorders.

This talk will review the general mechanism by which autoimmune diseases occur and discuss the pros and cons of conventional pharmaceutical therapies as they pertain to autoimmune disease treatment. I will then examine the rational and design methodology for the proposed siRNA therapy and how it contrasts with contemporary methods for the treatment of these conditions. Additionally, the talk will compare the efficacy of multiple design strategies for such molecules by comparison over several metrics and discuss how this will be guiding future research.

Zoom ID: 950 2372 5230 (Password: cmsa)

—–
Subscribe to Harvard CMSA seminar videos (more to be uploaded):
https://www.youtube.com/channel/UCBmPO-OK1sa8T1oX_9aVhAg/playlists
https://www.youtube.com/channel/UCM06KiUOw1vRrmvD8U274Ww

For a fixed prime p and large n, what is the largest size of a subset of \mathbb{F}_p^n which does not contain a non-trivial solution to some given linear equation or system of linear equations? This is a fundamental question in additive combinatorics with a long history. While there are various different notions of “non-trivial solutions”, in this talk we say that a solution is non-trivial if all of its variables are distinct.

A particularly famous and important instance of the question above is the problem of bounding the largest size of a subset of \mathbb{F}_p^n which does not contain a three-term arithmetic progression. In 2016, Ellenberg and Gijswijt made a breakthrough on this problem and the approach in their proof was later generalized by Tao yielding what is now called the slice rank polynomial method. Unfortunately, for other instances of the question above, the slice rank polynomial method cannot handle the condition for the variables in a non-trivial solution to be distinct.

In this talk, we will first give a brief survey on the slice rank polynomial method and some of its applications, and we will then discuss two different results concerning the question above. These results combine the slice rank polynomial method with additional combinatorial ideas in order to handle the distinctness condition. We also discuss an application of one of these results to the Erdös-Ginzburg-Ziv problem in discrete geometry.