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2  3  CMSA EVENT: Computational Biology Symposium
10:00 AM3:50 PM May 3, 2021 On Monday, May 3rd the Harvard CMSA will be hosting a Computational Biology Symposium virtually on Zoom. Please visit the event webpage for the schedule and more information. The event poster is attached. Registration is free but required. Register here. Details on how to join the webinar will be sent to registered participants before the event. The speakers will be: Uri Alon, Weizmann Institute Elana Fertig, Johns Hopkins Martin Hemberg, Brigham and Women’s Hospital Peter Kharchenko, Harvard University Smita Krishnaswamy, Yale University John Marioni, EMBLEBI Eran Segal, Weizmann Institute Meromit Singer, Harvard Medical School
 4  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM May 4, 2021 LiebThirring inequalities are a mathematical expression of the uncertainty and exclusion principles in quantum mechanics. They were introduced by Lieb and Thirring in 1975 in their proof of stability of matter and have since played an important role in several areas of analysis and mathematical physics. We provide a gentle introduction to classical aspects of this subject and we also present some newer developments, concerning extensions of several inequalities in harmonic analysis to the setting of families of orthonormal functions. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Computer Science for Mathematicians: RankBased Independence Testing in Near Linear Time
11:30 AM12:30 PM May 4, 2021 In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonlyused test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time. We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk. Joint work with Calvin Leng. Zoom: https://harvard.zoom.us/j/98231541450  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM May 4, 2021  DIFFERENTIAL GEOMETRY SEMINAR
9:00 PM10:00 PM May 4, 2021 We are interested in smoothing of a degenerate CalabiYau variety or a pair (degenerate CY, sheaf). I will explain an algebraic framework for solving such smoothability problems. The idea is to glue local dg Lie algebras (or dg BatalinVilkovisky algebras), coming from suitable local models, to get a global object. The key observation is that while this object is only an almost dg Lie algebra (or predg Lie algebra), it is sufficient to prove unobstructedness of the associated MaurerCartan equation (a kind of BogomolovTianTodorov theorem) under suitable assumptions, so the former can be regarded as a singular version of the KodairaSpencer DGLA. Our framework applies to degenerate CY varieties previously studied by KawamataNamikawa and GrossSiebert, as well as a more general class of varieties called toroidal crossing spaces (by the recent work of FeltenFilipRuddat). This talk is based on joint works with Conan Leung, Ziming Ma and Y.H. Suen. Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09
 5  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Anomalies and Supersymmetry
8:00 PM9:30 PM May 5, 2021 Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or Rsymmetry. I will discuss how quantum anomalies in these symmetries produce the local BardeenZumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the noninvariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the WessZumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the WessZumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric ChernSimons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors. Zoom: https://harvard.zoom.us/j/977347126
 6  7  CMSA EVENT: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
11:00 AM5:00 PM May 7, 2021May 9, 2021 The aim of the workshop is to bring together a community of researchers in mathematics, computer science and data science who develop theoretical and computational models to characterize shapes and analysis of image data. The first half of the workshop will feature talks aimed at graduate students, newcomers and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications. Register here to attend this event To find out details about the event, visit the CMSA event page.
 8  CMSA EVENT: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
11:00 AM5:00 PM May 8, 2021May 9, 2021 The aim of the workshop is to bring together a community of researchers in mathematics, computer science and data science who develop theoretical and computational models to characterize shapes and analysis of image data. The first half of the workshop will feature talks aimed at graduate students, newcomers and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications. Register here to attend this event To find out details about the event, visit the CMSA event page.

9  CMSA EVENT: FRG Workshop on Geometric Methods for Analyzing Discrete Shapes
11:00 AM5:00 PM May 9, 2021May 9, 2021 The aim of the workshop is to bring together a community of researchers in mathematics, computer science and data science who develop theoretical and computational models to characterize shapes and analysis of image data. The first half of the workshop will feature talks aimed at graduate students, newcomers and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications. Register here to attend this event To find out details about the event, visit the CMSA event page.
 10  11  CMSA EVENT: CMSA Computer Science for Mathematicians: Computability Theory for Designing Machine Learning Algorithms
11:30 AM12:30 PM May 11, 2021 This talk is about learning from informant, a formal model for binary classification. Illustrating examples are linear separators and other uniformly decidable sets of formal languages. Due to the learning by enumeration technique by Gold the learning process can be assumed consistent when fullinformation is available. The original model can be adjusted towards the setting of deep learning. We investigate the learnability of the set of halfspaces by these incremental learners. Moreover, they have less learning power than the fullinformation variant by a fundamental proof technique due to Blum and Blum. This technique can also be used to separate consistency. Finally, we present recent results towards a better understanding of (strong) nonUshaped learning from binary labeled input data. To separate the syntactic variant, we employ an infinite recursion theorem by Case. Zoom: https://harvard.zoom.us/j/98231541450
 12  CMSA EVENT: CMSA Strongly Correlated Quantum Materials and HighTemperature Superconductors Series: A unified theoretical perspective on the cuprate phase diagram
10:30 AM12:00 PM May 12, 2021 Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical meanfield theory sheds light on the pseudogap, on the quantumcritical point and on dwave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from halffilling. I will also briefly comment on what information theoretic measures tell us about this problem. Zoom: https://harvard.zoom.us/j/977347126
 13  CMSA EVENT: CMSA Interdisciplinary Science Seminar: A Tight Deterministic Algorithm for the Submodular Multiple Knapsack Problem
9:00 AM10:00 AM May 13, 2021 Submodular function maximization has been a central topic in the theoretical computer science community over the last decade. Plenty of wellperforming approximation algorithms have been designed for the maximization of (monotone or nonmonotone) submodular functions over a variety of constraints. In this talk, we consider the submodular multiple knapsack problem (SMKP), which is the submodular version of the wellstudied multiple knapsack problem (MKP). Roughly speaking, the problem asks to maximize a monotone submodular function over multiple bins (knapsacks). Recently, Fairstein et al. (ESA20) presented a tight (1−1/e−ϵ)approximation randomized algorithm for SMKP. Their algorithm is based on the continuous greedy technique which inherently involves randomness. However, the deterministic algorithm of this problem has not been understood very well previously. In this paper, we present a tight (1−1/e−ϵ) deterministic algorithm for SMKP. Our algorithm is based on reducing SMKP to an exponentialsize submodular maximizaion problem over a special partition matroid which enjoys a tight deterministic algorithm. We develop several techniques to mimic the algorithm, leading to a tight deterministic approximation for SMKP. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Quantum Information Theory of the Gravitational Anomaly
10:30 AM12:00 PM May 13, 2021 I am going to argue that the nonvanishing gravitational anomaly in 2D CFT obstructs the existence of the welldefined notion of entanglement. As a corollary, we will also see that the nonvanishing gravitational anomaly means the nonexistence of the lattice regulator generalizing the NielsenNinomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320]. Zoom: https://harvard.zoom.us/j/977347126
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16  17  18  CMSA EVENT: CMSA Computer Science for Mathematicians: Optimization Methods in AI and Machine Learning: Submodularity and Beyond
11:30 AM12:30 PM May 18, 2021 Several optimization problems in AI Machine Learning can be solved with the maximization of functions that exhibit natural diminishing returns. Examples include feature selection for Generalized Linear Models, Data Summarization, and Bayesian experimental design. By leveraging diminishing returns, it is possible to design efficient approximation algorithms for these problems.One of the simplest notions of diminishing returns is submodularity. Submodular functions are particularly interesting, because they admit simple, yet nontrivial, polynomialtime approximation algorithms. In recent years, several definitions have been proposed, to generalize the notion of submodularity. A study of these generalized functions lead to the design of efficient approximation algorithms for nonconvex problems.In this talk, I will discuss the notion of submodularity, and illustrate relevant results on this topic, including new interesting combinatorial algorithms. I will also talk about generalizations of this notion to continuous domains, and how they translate into first and secondorder conditions. I will discuss how these notions pertain interesting problems in AI Machine Learning. Zoom: https://harvard.zoom.us/j/98231541450
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23  24  25  CMSA EVENT: CMSA Math Science Literature Lecture Series
9:00 AM10:30 AM May 25, 2021 TITLE: Ktheory and characteristic classes in topology and complex geometry (a tribute to Atiyah and Hirzebruch) ABSTRACT: We will discuss the Ktheory of complex vector bundles on topological spaces and of holomorphic vector bundles on complex manifolds. A central question is the relationship between Ktheory and cohomology. This is done in topology by constructing characteristic classes, but other constructions appear in the holomorphic or algebraic context. We will discuss the Hirzebruch RiemannRoch formula, the AtiyahHirzebruch spectral sequence, the role of complex cobordism, and other tools developed later on, like the BlochOgus spectral sequence. Talk chair: Baohua Fu Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.” For more information, please visit the event page.  COLLOQUIUMS
3:00 PM4:00 PM May 25, 2021 Title: New Structures in Gravitational Waves Abstract: Mathematical General Relativity (GR) explores the structures and resulting dynamics of gravitational systems. These are described by the Einstein equations, which can be written as a system of nonlinear, hyperbolic partial differential equations. Recent years have seen fruitful interactions between physical questions and geometric analysis, sparking new breakthroughs, in particular related to gravitational radiation. Gravitational waves transport information from faraway regions of the Universe. They were observed for the first time by Advanced LIGO in 2015. So far, most studies in GR have been devoted to sources like binary black hole mergers or generally to sources that are stationary outside of a compact set. However, when extended neutrino halos are present, the situation changes. Mathematically, we describe these systems by asymptoticallyflat manifolds solving the Einstein equations. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields fall off more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects (permanent change of the spacetime) that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations. Registration is required to receive the Zoom information. Please go here to register.
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