11/10/2020 Computer Science for Mathematicians
2020-11-10 11:30 - 12:30 (America/New_York)

11/11/2020 Quantum Matter Seminar
2020-11-11 10:30 - 12:00

Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction, spatial graph dynamics, and symbolic mathematics
2020-11-11 15:00 - 16:00 | Virtual
Speaker: Eric Mjolsness, Departments of Computer Science and Mathematics, UC Irvine
Title: Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction, spatial graph dynamics, and symbolic mathematics
Abstract: The complexity of biological systems (among others) makes demands on the complexity of the mathematical modeling enterprise that could be satisfied with mathematical artificially intelligence of both symbolic and numerical flavors. Technologies that I think will be fruitful in this regard include (1) the use of machine learning to bridge spatiotemporal scales, which I will illustrate with the “Dynamic Boltzmann Distribution” method for learning model reduction of stochastic spatial biochemical networks and the “Graph Prolongation Convolutional Network” approach to course-graining the biophysics of microtubules; (2) a meta-language for stochastic spatial graph dynamics, “Dynamical Graph Grammars”, that can represent structure-changing processes including microtubule dynamics and that has an underlying combinatorial theory related to operator algebras; and (3) an integrative conceptual architecture of typed symbolic modeling languages and structure-preserving maps between them, including model reduction and implementation maps.

11/11/2020 RM&PT Seminar
2020-11-11 15:00 - 16:00

11/12/2020 Condensed Matter Seminar
2020-11-12 10:30 - 12:00

CMSA Math-Science Literature Lecture: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions
2020-11-13 08:00 - 09:30 | Virtual
Edward Witten (IAS)
Title: Knot Invariants From Gauge Theory in Three, Four, and Five Dimensions
Abstract: I will explain connections between a sequence of theories in two, three, four, and five dimensions and describe how these theories are related to the Jones polynomial of a knot and its categorification.
Talk chair: Cliff Taubes
Video

CMSA Math-Science Literature Lecture: Classical and quantum integrable systems in enumerative geometry
2020-11-16 08:00 - 09:30 | Virtual
Andrei Okounkov (Columbia University)
Title: Classical and quantum integrable systems in enumerative geometry
Abstract: For more than a quarter of a century, thanks to the ideas and questions originating in modern high-energy physics, there has been a very fruitful interplay between enumerative geometry and integrable system, both classical and quantum. While it is impossible to summarize even the most important aspects of this interplay in one talk, I will try to highlight a few logical points with the goal to explain the place and the role of certain more recent developments.
Talk chair: Cumrun Vafa
Video

11/16/2020 Mathematical Physics Seminar
2020-11-16 10:00 - 11:00

11/17/2020 Computer Science for Mathematicians
2020-11-17 11:30 - 12:30

CMSA Math-Science Literature Lecture: Log Calabi-Yau fibrations
2020-11-18 08:00 - 09:30 | Virtual
Caucher Birkar (University of Cambridge)
Title: Log Calabi-Yau fibrations
Abstract: Fano and Calabi-Yau varieties play a fundamental role in algebraic geometry, differential geometry, arithmetic geometry, mathematical physics, etc. The notion of log Calabi-Yau fibration unifies Fano and Calabi-Yau varieties, their fibrations, as well as their local birational counterparts such as flips and singularities. Such fibrations can be examined from many different perspectives. The purpose of this talk is to introduce the theory of log Calabi-Yau fibrations, to remind some known results, and to state some open problems.
Video

Re-pricing avalanches
2020-11-18 09:45 - 11:00 | Virtual
Speaker: Jose A. Scheinkman (Columbia)

Title: Re-pricing avalanches

Abstract: Monthly aggregate price changes exhibit chronic fluctuations but the aggregate shocks that drive these fluctuations are often elusive. Macroeconomic models often add stochastic macro-level shocks such as technology shocks or monetary policy shocks to produce these aggregate fluctuations. In this paper, we show that a state-dependent pricing model with a large but finite number of firms is capable of generating large fluctuations in the number of firms that adjust prices in response to an idiosyncratic shock to a firm’s cost of price adjustment. These fluctuations, in turn, cause fluctuations in aggregate price changes even in the absence of aggregate shocks. (Joint work with Makoto Nirei.)

11/18/2020 Strongly Correlated Quantum Materials
2020-11-18 10:30 - 12:00

11/18/2020 RMPT
2020-11-18 14:00 - 15:00

Universes as Big Data, or Machine-Learning Mathematical Structures
2020-11-18 15:00 - 16:00 | Virtual
Speaker: Yang-Hui He, Oxford University, City University of London and Nankai University
Title: Universes as Big Data, or Machine-Learning Mathematical Structures
Abstract: We review how historically the problem of string phenomenology lead theoretical physics first to algebraic/differetial geometry, and then to computational geometry, and now to data science and AI. With the concrete playground of the Calabi-Yau landscape, accumulated by the collaboration of physicists, mathematicians and computer scientists over the last 4 decades, we show how the latest techniques in machine-learning can help explore problems of physical and mathematical interest, from geometry, to group theory, to combinatorics and number theory.

11/19/20 Strongly Correlated Quantum Materials
2020-11-19 11:30 - 12:00

CMSA Math-Science Literature Lecture: Homotopy spectra and Diophantine equations
2020-11-20 08:00 - 09:30 | Virtual
Yuri Manin (Max Planck Institute for Mathematics)
Title: Homotopy spectra and Diophantine equations
Abstract: For a long stretch of time in the history of mathematics, Number Theory and Topology formed vast, but disjoint domains of mathematical knowledge. Origins of number theory can be traced back to the Babylonian clay tablet Plimpton 322 (about 1800 BC) that contained a list of integer solutions of the “Diophantine” equation $a^2+b^2=c^2$: archetypal theme of number theory, named after Diophantus of Alexandria (about 250 BC). Topology was born much later, but arguably, its cousin — modern measure theory, — goes back to Archimedes, author of Psammites (“Sand Reckoner”), who was approximately a contemporary of Diophantus. In modern language, Archimedes measures the volume of observable universe by counting the number of small grains of sand necessary to fill this volume. Of course, many qualitative geometric models and quantitative estimates of the relevant distances precede his calculations. Moreover, since the estimated numbers of grains of sand are quite large (about $10^{64}$), Archimedes had to invent and describe a system of notation for large numbers going far outside the possibilities of any of the standard ancient systems. The construction of the first bridge between number theory and topology was accomplished only about fifty years ago: it is the theory of spectra in stable homotopy theory. In particular, it connects $Z$, the initial object in the theory of commutative rings, with the sphere spectrum $S$. This connection poses the challenge: discover a new information in number theory using the developed independently machinery of homotopy theory. In this talk based upon the authors’ (Yu. Manin and M. Marcolli) joint research project, I suggest to apply homotopy spectra to the problem of distribution of rational points upon algebraic manifolds.
Talk chair: Michael Hopkins
Slides | Video

Members’ Seminar
2020-11-20 15:02 - 2021-01-01 15:02
The CMSA Members’ Seminar will occur every Friday at 9:30am ET on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series. Please email the seminar organizers to obtain a link. This year’s seminar is organized by Tianqi Wu. The Schedule will be updated below.
Previous seminars can be found here.
Spring 2021:

Date
Speaker
Title/Abstract

1/29/2021
Cancelled

2/5/2021
Itamar Shamir
Title: Boundary CFT and conformal anomalies
Abstract: Boundary and defects in quantum field theory play an important role in many recent developments in theoretical physics. I will discuss such objects in the setting of conformal field theories, focusing mainly on conformal anomalies. Boundaries or defects can support various kinds of conformal anomalies on their world volume. Perhaps the one which is of greatest theoretical importance is associated with the Euler density in even dimensions. I will show how this anomaly is related to the one point function of exactly marginal deformations and how it arises explicitly from various correlation functions.

2/12/2021
Louis Fan
Title: Joint distribution of Busemann functions in corner growth models
Abstract: The 1+1 dimensional corner growth model with exponential weights is a centrally important exactly solvable model in the Kardar-Parisi-Zhang class of statistical mechanical models. While significant progress has been made on the fluctuations of the growing random shape, understanding of the optimal paths, or geodesics, is less developed. The Busemann function is a useful analytical tool for studying geodesics. We present the joint distribution of the Busemann functions, simultaneously in all directions of growth, in terms of mappings that represent FIFO (first-in-first-out) queues. As applications of this description we derive a marked point process representation for the Busemann function across a single lattice edge and point out its implication on structure of semi-infinite geodesics. This is joint work with Timo Seppäläinen.

2/19/2021
Daniel Junghans
Title: Control issues of the KKLT scenario in string theory
Abstract: The simplest explanation for the observed accelerated expansion of the universe is that we live in a 4-dimensional de Sitter space. We analyze to which extent the KKLT proposal for the construction of such de Sitter vacua in string theory is quantitatively controlled. As our main finding, we uncover and quantify an issue which one may want to call the “singular-bulk problem”. In particular, we show that, generically, a significant part of the manifold on which string theory is compactified in the KKLT scenario becomes singular. This implies a loss of control over the supergravity approximation on which the construction relies.

2/26/2021
Tsung-Ju Lee
Title: SYZ fibrations and complex affine structures
Abstract: Strominger–Yau–Zaslow conjecture has been a guiding principle in mirror symmetry. The conjecture predicts the existence of special Lagrangian torus fibrations of a Calabi–Yau manifold near a large complex structure limit point. Moreover, the mirror is given by the dual fibrations and the Ricci-flat metric is obtained from the semi-flat metric with corrections from holomorphic discs whose boundaries lie in a special Lagrangian fiber. By a result of Collins–Jacob–Lin, the complement of a smooth elliptic curve in the projective plane admits a SYZ fibration. In this talk, I will explain how to compute the complex affine structure induced from this SYZ fibration and show that it agrees with the affine structure used in Carl–Pumperla–Siebert. This is based on a joint work with Siu-Cheong Lau and Yu-Shen Lin.

3/5/2021
Cancelled

3/11/2021
9:00pm ET
Ryan Thorngren
Title: Symmetry protected topological phases, anomalies, and their classification
Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

3/18/2021
9:00pm ET
Ryan Thorngren
Title: Symmetry protected topological phases, anomalies, and their classification
Abstract: I will give an overview of some mathematical aspects of the subject of symmetry protected topological phases (SPTs), especially as their theory relates to index theorems in geometry, cobordism of manifolds, and group cohomology.

3/26/2021
8:30am ET
Aghil Alaee
Title: Rich extra dimensions are hidden inside black holes
Abstract: In this talk, I present an argument that shows why it is difficult to see rich extra dimensions in the Universe.

4/2/2021
8:30am ET
Enno Keßler
Title: Super Stable Maps of Genus Zero
Abstract: I will report on a supergeometric generalization of J-holomorphic curves. Supergeometry is a mathematical theory of geometric spaces with anti-commuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. Super J-holomorphic curves and super stable maps couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants.

4/9/2021
Juven Wang
Video
Title: Ultra Unification
Abstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). In this work, we propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly matching and cobordism constraints (especially from the baryon minus lepton number B − L and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase), or right-handed neutrinos, or their combinations. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate more on the nonperturbative global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.

4/16/2021
Sergiy Verstyuk
Title: Deep learning methods for economics
Abstract: The talk discusses some recent developments in neural network models and their applicability to problems in international economics as well as macro-via-micro economics. Along the way, interpretability of neural networks features prominently.

4/23/2021
Yifan Wang
Title: Virtues of Defects in Quantum Field Theories
Abstract: Defects appear ubiquitously in many-body quantum systems as boundaries and impurities. They participate inextricably in the quantum dynamics and give rise to novel phase transitions and critical phenomena. Quantum field theory provides the natural framework to tackle these problems, where defects define extended operators over sub-manifolds of the spacetime and enrich the usual operator algebra. Much of the recent progress in quantum field theory has been driven by the exploration of general structures in this extended operator algebra, precision studies of defect observables, and the implications thereof for strongly coupled dynamics. In this talk, I will review selected developments along this line that enhance our understanding of concrete models in condensed matter and particle physics, and that open new windows to nonperturbative effects in quantum gravity.

4/30/2021
Yun Shi
Title: D-critical locus structure for local toric Calabi-Yau 3-fold
Abstract: Donaldson-Thomas (DT) theory is an enumerative theory which produces a count of ideal sheaves of 1-dimensional subschemes on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will give a brief introduction to motivic DT theory following the definition of Bussi-Joyce-Meinhardt, in particular the role of d-critical locus structure in the definition of motivic DT invariant. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint work in progress with Sheldon Katz.

5/7/2021
Thérèse Yingying Wu
Title: Topological aspects of Z/2Z eigenfunctions for the Laplacian on S^2
Abstract: In this talk, I will present recent work with C. Taubes on an eigenvalue problem for the Laplacian on the round 2-sphere associated with a configuration of an even number of distinct points on that sphere, denoted as C_2n. I will report our preliminary findings on how eigenvalues and eigenfunctions change as a function of the configuration space. I will also discuss how the compactification of C_2n is connected to the moduli space of algebraic curves (joint work with S.-T. Yau). There is a supergeometry tie-in too.

5/14/2021
Du Pei
Title: Three applications of TQFTs
Abstract: Topological quantum field theories (TQFTs) often serve as a bridge between physics and mathematics. In this talk, I will illustrate how TQFTs that arise in physics can help to shed light on 1) the quantization of moduli spaces 2) quantum invariants of 3-manifolds, and 3) smooth structures on 4-manifolds.

5/21/2021
Farzan Vafa
Title: Active nematic defects and epithelial morphogenesis
Abstract: Inspired by recent experiments that highlight the role of topological defects in morphogenesis, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture (a rank 2 symmetric traceless tensor). Allowing the surface to evolve via relaxational dynamics (gradient flow) leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects, and cells accumulate at positive defects and are depleted at negative defects. We also show that activity stabilizes a bound $+1$ defect state by creating an incipient tentacle, while a bound $+1$ defect state surrounded by two $-1/2$ defects can create a stationary ring configuration of tentacles, consistent with experimental observations. The talk is based on a recent paper with L Mahadevan [arXiv:2105.0106].

Fall 2020:

Date
Speaker
Title/Abstract

9/11/2020
Moran Koren
Title: Observational Learning and Inefficiencies in Waitlists
Abstract: Many scarce resources are allocated through waitlists without monetary transfers. We consider a model, in which objects with heterogeneous qualities are offered to strategic agents through a waitlist in a first-come-first-serve manner. Agents, upon receiving an offer, accept or reject it based on both a private signal about the quality of the object and the decisions of agents ahead of them on the list. This model combines observational learning and dynamic incentives, two features that have been studied separately. We characterize the equilibrium and quantify the inefficiency that arises due to herding and selectivity. We find that objects with intermediate expected quality are discarded while objects with a lower expected quality may be accepted. These findings help in understanding the reasons for the substantial discard rate of transplant organs of various qualities despite the large shortage of organ supply.

9/18/2020
Michael Douglas
Title: A talk in two parts, on strings and on computers and math
Abstract: I am dividing my time between two broad topics. The first is string theory, mostly topics in geometry and compactification. I will describe my current work on numerical Ricci flat metrics, and list many open research questions. The second is computation and artificial intelligence. I will introduce transformer models (Bert,GPT) which have led to breakthroughs on natural language processing, describe their potential for helping us do math, and sketch some related theoretical problems.

9/25/2020
Cancelled – Math Science Lecture

10/2/2020
Cancelled – Math Science Lecture

10/9/2020
Wai Tong (Louis) Fan
Title: Stochastic PDE as scaling limits of interacting particle systems
Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models.
In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE. These connections also explain how stochastic partial differential equations (SPDE) arise naturally under a suitable choice of level of detail in modeling complex systems. I will also present some novel scaling limits including SPDE on graphs and coupled SPDE. These SPDE not only interpolate between particle models and PDE, but also quantify the source and the order of magnitude of stochasticity. Scaling limit theorems and new duality formulas are obtained for these SPDE, which connect phenomena across scales and offer insights about the genealogies and the time-asymptotic properties of the underlying population dynamics. Joint work with Rick Durrett.

10/16/2020
Tianqi Wu
Title: Koebe circle domain conjecture and the Weyl problem in hyperbolic 3-space
Abstract: In 1908, Paul Koebe conjectured that every open connected set in the plane is conformally diffeomorphic to an open connected set whose boundary components are either round circles or points. The Weyl problem, in the hyperbolic setting, asks for isometric embedding of surfaces of curvature at least -1 into the hyperbolic 3-space. We show that there are close relationships among the Koebe conjecture, the Weyl problem and the work of Alexandrov and Thurston on convex surfaces. This is a joint work with Feng Luo.

10/23/2020
Changji Xu
Title: Random Walk Among Bernoulli Obstacles
Abstract: Place an obstacle with probability $1 – p$ independently at each vertex of $mathbb Z^d$ and consider a simple symmetric random walk that is killed upon hitting one of the obstacles. This is called random walk among Bernoulli obstacles. The most prominent feature of this model is a strong localization effect: the random walk will be localized in a very small region conditional on the event that it survives for a long time. In this talk, we will discuss some recent results about the behaviors of the conditional random walk, in quenched, annealed, and biased settings.

10/30/2020
Michael Simkin
Title: The differential equation method in Banach spaces and the $n$-queens problem
Abstract: The differential equation method is a powerful tool used to study the evolution of random combinatorial processes. By showing that the process is likely to follow the trajectory of an ODE, one can study the deterministic ODE rather than the random process directly. We extend this method to ODEs in infinite-dimensional Banach spaces.
We apply this tool to the classical $n$-queens problem: Let $Q(n)$ be the number of placements of $n$ non-attacking chess queens on an $n times n$ board. Consider the following random process: Begin with an empty board. For as long as possible choose, uniformly at random, a space with no queens in its row, column, or either diagonal, and place on it a queen. We associate the process with an abstract ODE. By analyzing the ODE we conclude that the process almost succeeds in placing $n$ queens on the board. Furthermore, we can obtain a complete $n$-queens placement by making only a few changes to the board. By counting the number of choices available at each step we conclude that $Q(n) geq (n/C)^n$, for a constant $C>0$ associated with the ODE. This is optimal up to the value of $C$.

11/6/2020
Kenji Kawaguchi
Title: Deep learning: theoretical results on optimization and mixup
Abstract: Deep neural networks have achieved significant empirical success in many fields, including the fields of computer vision, machine learning, and artificial intelligence. Along with its empirical success, deep learning has been theoretically shown to be attractive in terms of its expressive power. However, the theory of the expressive power does not ensure that we can efficiently find an optimal solution in terms of optimization, robustness, and generalization, during the optimization process of a neural network. In this talk, I will discuss some theoretical results on optimization and the effect of mixup on robustness and generalization.

11/13/2020
Omri Ben-Eliezer
Title: Sampling in an adversarial environment
Abstract: How many samples does one need to take from a large population in order to truthfully “represent” the population? While this cornerstone question in statistics is very well understood when the population is fixed in advance, many situations in modern data analysis exhibit a very different behavior: the population interacts with and is affected by the sampling process. In such situations, the existing statistical literature does not apply.
We propose a new sequential adversarial model capturing these situations, where future data might depend on previously sampled elements; we then prove uniform laws of large numbers in this adversarial model. The results, techniques, and applications reveal close connections to various areas in mathematics and computer science, including VC theory, discrepancy theory, online learning, streaming algorithms, and computational geometry.
Based on joint works with Noga Alon, Yuval Dagan, Shay Moran, Moni Naor, and Eylon Yogev.

11/20/2020
Charles Doran
Title: The Calabi-Yau Geometry of Feynman Integrals
Abstract: Over the past 30 years Calabi-Yau manifolds have proven to be the key geometric structures behind string theory and its variants. In this talk, I will show how the geometry and moduli of Calabi-Yau manifolds provide a new framework for understanding and computing Feynman integrals. An important organizational principle is provided by mirror symmetry, and specifically the DHT mirror correspondence. This is joint work with Andrey Novoseltsev and Pierre Vanhove.

Colloquia & Seminars,Seminars

CMSA Math-Science Literature Lecture: Noncommutative Geometry, the Spectral Aspect
2020-11-23 08:00 - 09:30 | Virtual
Alain Connes (Collège de France)
Title: Noncommutative Geometry, the Spectral Aspect
Abstract: This talk will be a survey of the spectral side of noncommutative geometry, presenting the new paradigm of spectral triples and showing its relevance for the fine structure of space-time, its large scale structure and also in number theory in connection with the zeros of the Riemann zeta function.
Talk chair: Peter Kronheimer
Video

CMSA Math-Science Literature Lecture: Subfactors–in Memory of Vaughan Jones
2020-11-23 10:00 - 11:30 | Virtual
Zhengwei Liu (Tsinghua University)
Title: Subfactors–in Memory of Vaughan Jones
Abstract: Jones initiated modern subfactor theory in the early 1980s and investigated this area for his whole academic life. Subfactor theory has both deep and broad connections with various areas in mathematics and physics. One well-known peak in the development of subfactor theory is the discovery of the Jones polynomial, for which Jones won the Fields Medal in 1990. Let us travel back to the dark room at the beginning of the story, to appreciate how radically our viewpoint has changed.
Talk chair: Arthur Jaffe
Slides | Video

11/23/2020 Mathematical Physics Seminar
2020-11-23 11:30 - 12:30

11/24/2020 Computer Science for Mathematicians
2020-11-24 11:30 - 12:30

CMSA Math-Science Literature Lecture: Theorems of Torelli type
2020-11-25 09:00 - 10:30 | Virtual
Eduard Jacob Neven Looijenga (Tsinghua University & Utrecht University)
Title: Theorems of Torelli type
Abstract: Given a closed manifold of even dimension 2n, then Hodge showed around 1950 that a kählerian complex structure on that manifold determines a decomposition of its complex cohomology. This decomposition, which can potentially vary continuously with the complex structure, extracts from a non-linear given, linear data. It can contain a lot of information. When there is essentially no loss of data in this process, we say that the Torelli theorem holds. We review the underlying theory and then survey some cases where this is the case. This will include the classical case n=1, but the emphasis will be on K3 manifolds (n=2) and more generally, on hyperkählerian manifolds. These cases stand out, since one can then also tell which decompositions occur.
Talk chair: Gerard van der Geer
Video

11/25/2020 Strongly Correlated Materials
2020-11-25 10:30 - 12:00

CMSA Math-Science Literature Lecture: Is relativity compatible with quantum theory?
2020-12-02 08:00 - 09:30 | Virtual
Arthur Jaffe (Harvard University)
Title: Is relativity compatible with quantum theory?
Abstract: We review the background, mathematical progress, and open questions in the effort to determine whether one can combine quantum mechanics, special relativity, and interaction together into one mathematical theory. This field of mathematics is known as “constructive quantum field theory.” Physicists believe that such a theory describes experimental measurements made over a 70 year period and now refined to 13-decimal-point precision—the most accurate experiments ever performed.
Talk chair: Zhengwei Liu
Video

12/2/2020 Strongly Correlated Quantum Materials
2020-12-02 12:00 - 13:30

12/2/2020 Random Matrix and Probability Theory
2020-12-02 14:00 - 15:00 | Virtual

12/3/2020 Quantum Matter Seminar
2020-12-03 10:30 - 12:00

CMSA Math-Science Literature Lecture: Michael Atiyah: Geometry and Physics
2020-12-04 08:00 - 09:30 | Virtual
Nigel Hitchin (University of Oxford)
Title: Michael Atiyah: Geometry and Physics
Abstract: In mid-career, as an internationally renowned mathematician, Michael Atiyah discovered that some problems in physics responded to current work in algebraic geometry and this set him on a path to develop an active interface between mathematics and physics which was formative in the links which are so active today. The talk will focus, in a fairly basic fashion, on some examples of this interaction, which involved both applying physical ideas to solve mathematical problems and introducing mathematical ideas to physicists.
Talk chair: Peter Kronheimer
Video

12/7/2020 Math Physics Seminar
2020-12-07 10:30 - 11:30

12/9/2020 Strongly Correlated Quantum Materials
2020-12-09 10:30 - 12:00
