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February  1  CMSA EVENT: CMSA Mathematical Physics Seminar: Mathematical supergravity and its applications to differential geometry
10:00 AM11:00 AM March 1, 2021 I will discuss the recent developments in the mathematical theory of supergravity that lay the mathematical foundations of the universal bosonic sector of fourdimensional ungauged supergravity and its Killing spinor equations in a differentialgeometric framework. I will provide the necessary context and background. explaining the results pedagogically from scratch and highlighting several open mathematical problems which arise in the mathematical theory of supergravity, as well as some of its potential mathematical applications. Work in collaboration with Vicente Cortés and Calin Lazaroiu. Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09  COLLOQUIUMS
3:00 PM4:00 PM March 1, 2021 Title: Robustness Meets Algorithms Abstract: Starting from the seminal works of Tukey (1960) and Huber (1964), the field of robust statistics asks: Are there estimators that probably work in the presence of noise? The trouble is that all known provably robust estimators are also hard to compute in highdimensions. Here, we study a fundamental problem in robust statistics, posed in various forms in the above works. Given corrupted samples from a highdimensional Gaussian, are there efficient algorithms to accurately estimate its parameters? We give the first algorithm that is able to tolerate a constant fraction of corruptions that is independent of the dimension. Moreover, we give a general recipe for detecting and correcting corruptions based on tensorspectral techniques that are applicable to many other problems. I will also discuss how this work fits into the broader agenda of developing mathematical and algorithmic foundations for modern machine learning. Registration is required to receive the Zoom information Register here to attend
 2  DIFFERENTIAL GEOMETRY SEMINAR
8:00 AM9:00 AM March 2, 2021 A disc potential function plays an important role in studying a symplectic manifold and its Lagrangian submanifolds. In this talk, I will explain how to compute the disc potential function of quadrics. The potential function provides the Landau—Ginzburg mirror, which agrees with Przyjalkowski’s mirror and a cluster chart of Pech—Rietsch—Williams’ mirror Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM March 2, 2021 Polyakov introduced Liouville Conformal Field theory (LCFT) in 1981 as a way to put a naturalmeasure on the set of Riemannian metrics over a two dimensional manifold. Ever since, the work of Polyakov has echoed in various branches of physics and mathematics, ranging from string theory to probability theory and geometry. In the context of 2D quantum gravity models, LCFT is related through the KnizhnikPolyakovZamolodchikov relationsto the scaling limit of Random Planar Maps and through the AldayGaiottoTachikava correspondence LCFT is conjecturally related to certain 4D YangMills theories. Through the work of Dorn, Otto, Zamolodchikov and Zamolodchikov and Teschner LCFT is believed to be to a certain extent integrable. I will review a probabilistic construction of LCFT and recent proofs concerning the integrability of LCFT developed together with F. David, C. Guillarmou, R. Rhodes and V. Vargas. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Computer Science for Mathematicians: Randomized Dimensionality Reduction for Clustering
11:30 AM12:30 PM March 2, 2021 Random dimensionality reduction is a versatile tool for speeding up algorithms for highdimensional problems. We study its application to two clustering problems: the facility location problem, and the singlelink hierarchical clustering problem, which is equivalent to computing the minimum spanning tree. We show that if we project the input pointset $X$ onto a random $d = O(d_X)$dimensional subspace (where $d_X$ is the doubling dimension of $X$), then the optimum facility location cost in the projected space approximates the original cost up to a constant factor. We show an analogous statement for minimum spanning tree, but with the dimension $d$ having an extra $\log \log n$ term and the approximation factor being arbitrarily close to $1$. Furthermore, we extend these results to approximating solutions instead of just their costs. Lastly, we provide experimental results to validate the quality of solutions and the speedup due to the dimensionality reduction. Unlike several previous papers studying this approach in the context of $k$means and $k$medians, our dimension bound does not depend on the number of clusters but only on the intrinsic dimensionality of $X$. Joint work with Shyam Narayanan, Piotr Indyk, Or Zamir. Zoom: https://harvard.zoom.us/j/98231541450  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM March 2, 2021 In complex algebraic geometry, the decomposition theorem asserts that semisimple geometric objects remain semisimple after taking direct images under proper algebraic maps. This was conjectured by Kashiwara and is proved by Mochizuki and Sabbah in a series of long papers via harmonic analysis and Dmodules. In this talk, I would like to explain a more geometric/topological approach in the case of semisimple local systems adapting de CataldoMigliorini. As a byproduct, we can recover a weak form of Saito’s decomposition theorem for variations of Hodge structures. Joint work in progress with Chuanhao Wei. Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09
 3  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Symmetryprotected sign problem and magic in quantum phases of matter
10:30 AM12:00 PM March 3, 2021 We introduce the concepts of a symmetryprotected sign problem and symmetryprotected magic, defined by the inability of symmetric finitedepth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, onedimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetryprotected sign problem, and twodimensional Z2 SPT states (e.g. LevinGu state) have both a symmetryprotected sign problem and magic. We also comment on the relation of a symmetryprotected sign problem to the computational wire property of onedimensional SPT states and the greater implications of our results for measurement based quantum computing. Zoom: https://harvard.zoom.us/j/977347126  CMSA EVENT: CMSA New Technologies in Mathematics: Neural Theorem Proving in Lean using Proof Artifact Cotraining and Language Models
3:00 PM4:00 PM March 3, 2021 Labeled data for imitation learning of theorem proving in large libraries of formalized mathematics is scarce as such libraries require years of concentrated effort by human specialists to be built. This is particularly challenging when applying large Transformer language models to tactic prediction, because the scaling of performance with respect to model size is quickly disrupted in the datascarce, easilyoverfitted regime. We propose PACT (Proof Artifact CoTraining), a general methodology for extracting abundant selfsupervised data from kernellevel proof terms for cotraining alongside the usual tactic prediction objective. We apply this methodology to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date. We instrument Lean with a neural theorem prover driven by a Transformer language model and show that PACT improves theorem proving success rate on a heldout suite of test theorems from 32\% to 48\%. Zoom: https://harvard.zoom.us/j/99018808011?pwd=SjRlbWFwVms5YVcwWURVN3R3S2tCUT09  NUMBER THEORY SEMINAR
3:00 PM4:00 PM March 3, 2021 In the talk, I will present an equidistribution result for families of (nondegenerate) subvarieties in a (general) family of abelian varieties. This extends a result of DeMarco and Mavraki for curves in fibered products of elliptic surfaces. Using this result, one can deduce a uniform version of the classical Bogomolov conjecture for curves embedded in their Jacobians, namely that the number of torsion points lying on them is uniformly bounded in the genus of the curve. This has been previously only known in a few select cases by work of David–Philippon and DeMarco–Krieger–Ye. Finally, one can obtain a rather uniform version of the MordellLang conjecture as well by complementing a result of Dimitrov–Gao–Habegger: The number of rational points on a smooth algebraic curve defined over a number field can be bounded solely in terms of its genus and the MordellWeil rank of its Jacobian. Again, this was previously known only under additional assumptions (Stoll, Katz–Rabinoff–ZureickBrown).
Zoom: https://harvard.zoom.us/j/99334398740 Password: The order of the permutation group on 9 elements.  OPEN NEIGHBORHOOD SEMINAR
4:30 PM5:30 PM March 3, 2021 An evil mathematician has kidnapped the Harvard Pilgrim! To win his freedom, a group of undergrads must each find their name in a row of boxes. The odds look dire—but we’ll use some probability theory and combinatorics to find a strategy that dramatically improves our chances. Can you help save our hapless mascot? Please go to the College Calendar to register.
 4  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Generalized ‘t Hooft anomalies in vectorlike theories
10:30 AM12:00 PM March 4, 2021 ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of stronglycoupled theories. Recently, it has been realized that higherform global symmetries can also become anomalous, leading to further constraints on the infrared dynamics. In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vectorlike asymptoticallyfree gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on stronglycoupled gauge theories. Then, I argue that the anomaly inflow can explain a nontrivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls. This phenomenon can be explicitly seen in a weaklycoupled model of QCD compactified on a small circle. Zoom: https://harvard.zoom.us/j/977347126
 5  ALGEBRAIC DYNAMICS SEMINAR
10:00 AM12:00 PM March 5, 2021 In the moduli space of one variable complex cubic polynomials with a marked critical point, given any $p \ge 1$, we prove that the loci formed by polynomials with the marked critical point periodic of period $p$ is an irreducible curve. Our methods rely on techniques used to study onecomplexdimensional parameter spaces. This is joint work with Matthieu Arfeux. Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for Zoom information.
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7  8  CMSA EVENT: CMSA Mathematical Physics Seminar: Virasoro constraints for stable pairs
10:00 AM11:00 AM March 8, 2021 The theory of stable pairs (PT) with descendents, defined on a 3fold X, is a sheaf theoretical curve counting theory. Conjecturally, it is equivalent to the GromovWitten (GW) theory of X via a universal (but intricate) transformation, so we can expect that the Virasoro conjecture on the GW side should have a parallel in the PT world. In joint work with A. Oblomkov, A. Okounkov, and R. Pandharipande, we formulated such a conjecture and proved it for toric 3folds in the stationary case. The Hilbert scheme of points on a surface S might be regarded as a component of the moduli space of stable pairs on S x P1, and the Virasoro conjecture predicts a new set of relations satisfied by tautological classes on S[n] which can be proven by reduction to the toric case. Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09  COLLOQUIUMS
3:00 PM4:00 PM March 8, 2021 Title: Topological Recursion and Enumerative Geometry Abstract: Given a holomorphic curve in the complex 2plane together with a suitably normalized symmetric meromorphic bilinear differential, the ChekhovEynardOrantin Topological Recursion defines an infinite sequence of symmetric meromorphic multilinear differentials W_{g,n} on the curve. In many examples, the invariants W_{g,n} provide answers to enumerative problems. I will describe Topological Recursion and present several examples in which the answers are Hodge integrals (which are intersection numbers on moduli of curves) or GromovWitten invariants (which are virtual counts of holomorphic maps from Riemann surfaces to a Kahler manifold). Registration is required to receive the Zoom information Register here to attend
 9  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM March 9, 2021 One of the most fascinating aspects about noncommutative spaces (aka von Neumann algebras), is the way their building data, which is often geometric in nature, impacts on the properties of their quantized symmetries. This is particularly the case for II_{1} factors, where symmetries are encoded by their subfactors of finite Jones index. I will discuss some results and open problems that illustrate the unique interplay between analysis and algebra/combinatorics entailed by this interdependence, that’s specific to subfactor theory. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Computer Science for Mathematicians: Optimal Mean Estimation without a Variance
11:30 AM12:30 PM March 9, 2021 Estimating the mean of a distribution from i.i.d samples is a fundamental statistical task. In this talk, we will focus on the highdimensional setting where we will design estimators achieving optimal recovery guarantees in terms of all relevant parameters. While optimal onedimensional estimators have been known since the 80s (Nemirovskii and Yudin ’83), optimal estimators in high dimensions have only been discovered recently beginning with the seminal work of Lugosi and Mendelson in 2017 and subsequent work has led to computationally efficient variants of these estimators (Hopkins 2018). We will discuss statistical and computational extensions of these results by developing optimal estimators for settings where the data distribution only obeys a finite fractional moment condition as opposed to the existence of a second moment as assumed previously. Joint work with Peter Bartlett, Nicolas Flammarion, Michael I. Jordan and Nilesh Tripuraneni. The talk will be based on the following papers: https://arxiv.org/abs/2011.12433, https://arxiv.org/abs/1902.01998. Zoom: https://harvard.zoom.us/j/98231541450  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM March 9, 2021 We will report on a recent joint work with Junyan Cao, cf. arXiv:2012.05063. The main topics we will discuss are revolving around the extension of pluricanonical forms defined on the central fiber of a family of Kaehler manifolds. For our results to hold we need the divisor of zeros of the said forms to be sufficiently “nice”, in a sense that will become clear during the talk. Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09
 10  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Supersymmetric quantum field theory with exotic symmetry in 3+1 dimensions and fermionic fracton phases
10:30 AM12:00 PM March 10, 2021 Fracton phases show exotic properties, such as subextensive entropy, local particlelike excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a selfduality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons. Zoom: https://harvard.zoom.us/j/977347126  CMSA EVENT: CMSA New Technologies in Mathematics: The Ramanujan Machine: Using Algorithms for the Discovery of Conjectures on Mathematical Constants
3:00 PM4:00 PM March 10, 2021 In the past, new conjectures about fundamental constants were discovered sporadically by famous mathematicians such as Newton, Euler, Gauss, and Ramanujan. The talk will present a different approach – a systematic algorithmic approach that discovers new mathematical conjectures on fundamental constants. We call this approach “the Ramanujan Machine”. The algorithms found dozens of wellknown formulas as well as previously unknown ones, such as continued fraction representations of π, e, Catalan’s constant, and values of the Riemann zeta function. Some of the conjectures are in retrospect simple to prove, whereas others remain so far unproven. We will discuss these puzzles and wider open questions that arose from this algorithmic investigation – specifically, a newlydiscovered algebraic structure that seems to generalize all the known formulas and connect between fundamental constants. We will also discuss two algorithms that proved useful in finding conjectures: a variant of the meetinthemiddle algorithm and a gradient descent algorithm tailored to the recurrent structure of continued fractions. Both algorithms are based on matching numerical values; consequently, they conjecture formulas without providing proofs or requiring prior knowledge of the underlying mathematical structure. This way, our approach reverses the conventional usage of sequential logic in formal proofs; instead, using numerical data to unveil mathematical structures and provide leads to further mathematical research. Zoom: https://harvard.zoom.us/j/99018808011?pwd=SjRlbWFwVms5YVcwWURVN3R3S2tCUT09  NUMBER THEORY SEMINAR
3:00 PM4:00 PM March 10, 2021
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3:00 PM4:00 PM March 16, 2021 Title: Recent progress on random field Ising model Abstract: Random field Ising model is a canonical example to study the effect of disorder on long range order. In 70’s, ImryMa predicted that in the presence of weak disorder, the longrange order persists at low temperatures in three dimensions and above but disappears in two dimensions. In this talk, I will review mathematical development surrounding this prediction, and I will focus on recent progress on exponential decay and on correlation length in two dimensions. The talk is based on a joint work with Jiaming Xia and a joint work with Mateo Wirth. Registration is required to receive the Zoom information Register here to attend
 17  18  19  ALGEBRAIC DYNAMICS SEMINAR
10:00 AM12:00 PM March 19, 2021 Let K be a complete and algebraically closed field, such as C or the padic field C_p, and let f\in K(z) be a rational function of degree d\geq 2. The map f is said to be hyperbolic if there is some metric on its Julia set with respect to which it is expanding. A celebrated 1983 theorem of Mane, Sad, and Sullivan shows that for K=C, hyperbolic maps are Jstable, meaning that nearby maps in moduli space have topologically conjugate dynamics on their Julia sets. In this talk, we show that if K is nonarchimedean, an a priori weaker boundedcontraction condition also yields Jstability. This project is joint work with Junghun Lee. Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for Zoom information.
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