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March  March  March  March  1  CMSA EVENT: CMSA Strongly Correlated Quantum Materials and HighTemperature Superconductors Series: Applied physics of highTc theories
9:00 AM10:30 AM April 1, 2021 Since the discovery of hightemperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics. Zoom: https://harvard.zoom.us/j/977347126  HARVARDMITBUBRANDEISNORTHEASTERN COLLOQUIUM
4:30 PM5:30 PM April 1, 2021 Many models in equilibrium statistical physics produce random fractal curves “at criticality.” I will discuss one particular model, the looperased random walk, which is closely related to uniform spanning trees and Laplacian motion, and survey what is known today including some more recent results. I will also discuss some of the important open problems and explain why the problem is hardest in exactly three dimensions. This talk is intended for a general mathematics audience and does not assume the audience knows the terms in the previous sentence. Zoom: https://northeastern.zoom.us/j/95962897745?pwd=UFFPV2sxUitpWGFZbVErM1kwY284Zz09 For password email Andrew McGuinness
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4  5  6  DIFFERENTIAL GEOMETRY SEMINAR
8:00 AM9:00 AM April 6, 2021 This talk will be about refined curve counting on local P^2, the noncompact CalabiYau 3fold total space of the canonical line bundle of the projective plane. I will explain how to construct quasimodular forms starting from Betti numbers of moduli spaces of dimension 1 coherent sheaves on P^2. This gives a proof of some stringy predictions about the refined topological string theory of local P^2 in the NekrasovShatashvili limit. Partly based on work with Honglu Fan, Shuai Guo, and Longting Wu. Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09  CMSA EVENT: CMSA Math Science Literature Lecture Series
9:00 AM10:30 AM April 6, 2021 TITLE: Isadore Singer’s Work on Analytic Torsion ABSTRACT: I will review two famous papers of Ray and Singer on analytic torsion written approximately half a century ago. Then I will sketch the influence of analytic torsion in a variety of areas of physics including anomalies, topological field theory, and string theory. Talk chair: Cumrun Vafa 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.  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 6, 2021 The space spanned by homotopy classes of free oriented loops on a 2manifold carries an interesting algebraic structure (a Lie bialgebra structure) due to Goldman and Turaev. This structure is defined in terms of intersections and selfintersections of planar curves. In the talk, we will explain a surprising link between the GaoldmanTuraev theory and the KashiwaraVergne problem on properties of the BakerCampbellHausdorff series. Important tools in establishing this link are the noncommutative divergence cocycle and a novel characterization of conjugacy classes in free Lie algebras in terms of cyclic words. The talk is based on joint works with N. Kawazumi, Y. Kuno and F. Naef. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 6, 2021 The space spanned by homotopy classes of free oriented loops on a 2manifold carries an interesting algebraic structure (a Lie bialgebra structure) due to Goldman and Turaev. This structure is defined in terms of intersections and selfintersections of planar curves. In the talk, we will explain a surprising link between the GaoldmanTuraev theory and the KashiwaraVergne problem on properties of the BakerCampbellHausdorff series. Important tools in establishing this link are the noncommutative divergence cocycle and a novel characterization of conjugacy classes in free Lie algebras in terms of cyclic words. The talk is based on joint works with N. Kawazumi, Y. Kuno and F. Naef. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Computer Science for Mathematicians: ConfidenceBudget Matching for Sequential Budgeted Learning
11:30 AM12:30 PM April 6, 2021 A core element in decisionmaking under uncertainty is the feedback on the quality of the performed actions. However, in many applications, such feedback is restricted. For example, in recommendation systems, repeatedly asking the user to provide feedback on the quality of recommendations will annoy them. In this work, we formalize decisionmaking problems with querying budget, where there is a (possibly timedependent) hard limit on the number of reward queries allowed. Specifically, we consider multiarmed bandits, linear bandits, and reinforcement learning problems. We start by analyzing the performance of `greedy’ algorithms that query a reward whenever they can. We show that in fully stochastic settings, doing so performs surprisingly well, but in the presence of any adversity, this might lead to linear regret. To overcome this issue, we propose the ConfidenceBudget Matching (CBM) principle that queries rewards when the confidence intervals are wider than the inverse square root of the available budget. We analyze the performance of CBM based algorithms in different settings and show that they perform well in the presence of adversity in the contexts, initial states, and budgets. Joint work with Yonathan Efroni, Aadirupa Saha and Shie Mannor. Zoom: https://harvard.zoom.us/j/98231541450
 7  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Higher Form Symmetries in string/Mtheory
10:30 AM12:00 PM April 7, 2021 In this talk, I will give an overview of recent developments in geometric constructions of field theory in string/Mtheory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/Mtheory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1form symmetries in class S, N=1 deformations thereof and the relation to confinement. Zoom: https://harvard.zoom.us/j/977347126  RANDOM MATRIX SEMINAR
2:00 PM3:00 PM April 7, 2021 In many problems in statistical learning, random matrix theory, and statistical physics, one needs to simulate dynamics on random matrix ensembles. A classical example is to use iterative methods to compute the extremal eigenvalues/eigenvectors of a (spiked) random matrix. Other examples include approximate message passing on dense random graphs, and gradient descent algorithms for solving learning and estimation problems with random initialization. We will show that all such dynamics can be simulated by an efficient matrixfree scheme, if the random matrix is drawn from an ensemble with translationinvariant properties. Examples of such ensembles include the i.i.d. Gaussian (i.e. the rectangular Ginibre) ensemble, the Haardistributed random orthogonal ensemble, the Gaussian orthogonal ensemble, and their complexvalued counterparts. A “direct” approach to the simulation, where one first generates a dense n × n matrix from the ensemble, requires at least O(n^2) resource in space and time. The new algorithm, named Householder Dice (HD), overcomes this O(n^2) bottleneck by using the principle of deferred decisions: rather than fixing the entire random matrix in advance, it lets the randomness unfold with the dynamics. At the heart of this matrixfree algorithm is an adaptive and recursive construction of (random) Householder reflectors. These orthogonal transformations exploit the group symmetry of the matrix ensembles, while simultaneously maintaining the statistical correlations induced by the dynamics. The memory and computation costs of the HD algorithm are O(nT) and O(n T^2), respectively, with T being the number of iterations. When T ≪ n, which is nearly always the case in practice, the new algorithm leads to significant reductions in runtime and memory footprint. Finally, the HD algorithm is not just a computational trick. I will show how its construction can serve as a simple proof technique for several problems in highdimensional estimation. Zoom: https://harvard.zoom.us/j/99333938108  NUMBER THEORY SEMINAR
3:00 PM4:00 PM April 7, 2021 The geometric Satake equivalence due to Lusztig, Drinfeld, Ginzburg, Mirković and Vilonen is an indispensable tool in the Langlands program. Versions of this equivalence are known for different cohomology theories such as Betti cohomology or algebraic Dmodules over characteristic zero fields and $\ell$adic cohomology over arbitrary fields. In this talk, I explain how to apply the theory of motivic complexes as developed by Voevodsky, Ayoub, CisinskiDéglise and many others to the construction of a motivic Satake equivalence. Under suitable cycle class maps, it recovers the classical equivalence. As dual group, one obtains a certain extension of the Langlands dual group by a one dimensional torus. A key step in the proof is the construction of intersection motives on affine Grassmannians. A direct consequence of their existence is an unconditional construction of ICChow groups of moduli stacks of shtukas. My hope is to obtain on the long run independenceof$\ell$ results in the work of V. Lafforgue on the Langlands correspondence for function fields. This is ongoing joint work with Jakob Scholbach from Münster. Zoom: https://harvard.zoom.us/j/99334398740 Password: The order of the permutation group on 9 elements.  CMSA EVENT: CMSA New Technologies in Mathematics: Type Theory from the Perspective of Artificial Intelligence
3:00 PM4:00 PM April 7, 2021 This talk will discuss dependent type theory from the perspective of artificial intelligence and cognitive science. From an artificial intelligence perspective it will be argued that type theory is central to defining the “game” of mathematics — an action space and reward structure for pure mathematics. From a cognitive science perspective type theory provides a model of the grammar of the colloquial (natural) language of mathematics. Of particular interest is the notion of a signatureaxiom structure class and the three fundamental notions of equality in mathematics — settheoretic equality between structure elements, isomorphism between structures, and Birkoff and Rota’s notion of cryptomorphism between structure classes. This talk will present a version of type theory based on settheoretic semantics and the 1930’s notion of structure and isomorphism given by the Bourbaki group of mathematicians. It will be argued that this “Bourbaki type theory” (BTT) is more natural and accessible to classically trained mathematicians than MartinLöf type theory (MLTT). BTT avoids the CurryHoward isomorphism and axiom J of MLTT. The talk will also discuss BTT as a model of MLTT. The BTT model is similar to the groupoid model in that propositional equality is interpreted as isomorphism but different in various details. The talk will also briefly mention initial thoughts in defining an action space and reward structure for a game of mathematics. Zoom: https://harvard.zoom.us/j/99018808011?pwd=SjRlbWFwVms5YVcwWURVN3R3S2tCUT09  OPEN NEIGHBORHOOD SEMINAR
4:30 PM5:30 PM April 7, 2021
 8  CMSA EVENT: CMSA Math Science Literature Lecture Series
9:00 AM10:30 AM April 8, 2021 TITLE: Quantum error correcting codes and fault tolerance ABSTRACT: We will go over the fundamentals of quantum error correction and fault tolerance and survey some of the recent developments in the field. Talk chair: Zhengwei Liu 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.  CMSA EVENT: CMSA Interdisciplinary Science Seminar: Supergeometry and Super Riemann Surfaces of Genus Zero
12:00 PM1:00 PM April 8, 2021 Supergeometry is a mathematical theory of geometric spaces with anticommuting coordinates and functions which is motivated by the concept of supersymmetry from theoretical physics. I will explain the functorial approach to supermanifolds by Molotkov and Sachse. Super Riemann surfaces are an interesting supergeometric generalization of Riemann surfaces. I will present a differential geometric approach to their classification in the case of genus zero and with NeveuSchwarz punctures. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Chiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics
1:00 PM2:30 PM April 8, 2021 In this talk, I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk, I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics. Zoom: https://harvard.zoom.us/j/977347126
 9  ALGEBRAIC DYNAMICS SEMINAR
10:00 AM12:00 PM April 9, 2021 Canonical heights are a standard tool of arithmetic dynamics over global fields. When studying families of dynamical systems, or systems over larger fields, however, there are significant geometric obstacles to constructing canonical heights. Either Northcott fails to hold, or the construction requires a model for the family with such strict properties (good reduction, minimality, extensions of rational maps,…) that such a model is unlikely to exist outside of very special settings. Instead, I’ll show how to resolve this problem using vectorvalued heights, first introduced in characteristic zero by Yuan and Zhang. These generalize Rvalued heights, produce canonical heights for any polarized dynamical system, and exhibit Northcott finiteness conditional on a strong nonisotriviality condition, generalizing work of LangNeron, Baker, and ChatzidakisHrushovski. This is achieved by working simultaneously over a system of models with much weaker requirements. As part of ongoing work, I’ll show how these arithmetic methods can produce results that hold over any field, and discuss how this can extend to quasiprojective varieties as well as projective varieties. Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for Zoom information.
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11  12  CMSA EVENT: CMSA Mathematical Physics Seminar: Networks and quantization
10:00 AM11:00 AM April 12, 2021 I will describe two quantization scenarios. The first scenario involves the construction of a quantum trace map computing a link “invariant” (with possible wallcrossing behavior) for links L in a 3manifold M, where M is a Riemann surface C times a real line. This construction unifies the computation of familiar link invariant with the refined counting of framed BPS states for line defects in 4d N=2 theories of class S. Certain networks on C play an important role in the construction. The second scenario concerns the study of Schroedinger equations and their higher order analogues, which could arise in the quantization of SeibergWitten curves in 4d N=2 theories. Here similarly certain networks play an important part in the exact WKB analysis for these Schroedingerlike equations. At the end of my talk I will also try to sketch a possibility to bridge these two scenarios. Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09
 13  CMSA EVENT: CMSA Math Science Literature Lecture Series
9:00 AM10:30 AM April 13, 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.  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 13, 2021 After giving a brief introduction to Membrane Theory and its matrix regularization, commenting on an inherent dynamical symmetry for all Mbranes (the related “reconstructionalgebra” for M=1, strings, being the Virasoro algebra), I will explain some very recent work, including the observation that supersymmetrizable systems canonically (i.e. more or less automatically) have a Laxpair formulation, with calculable rmatrix, – the appearance of infinitedimensional CKLalgebras naturally entering the double bracket equations of Quantum Minimal Surfaces (IKKT model) and the (“BFFS”) membrane matrix model. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM April 13, 2021 I will work on a CalabiYau 3fold X which satisfies the BogomolovGieseker conjecture of BayerMacr\`iToda for weak stability conditions, such as the quintic threefold. I will explain how wallcrossing with respect to weak stability conditions gives an expression of Joyce’s generalised DonaldsonThomas invariants counting Gieseker semistable sheaves of any rank greater than or equal to one on X in terms of those counting sheaves of rank 0 and pure dimension 2. This is joint work with Richard Thomas. Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09
 14  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Confinement and 1form Symmetries in 4d from 6d (2,0)
10:30 AM12:00 PM April 14, 2021 In this talk, I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk, I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics. Zoom: https://harvard.zoom.us/j/977347126  CMSA EVENT: CMSA New Technologies in Mathematics: A Bayesian neural network predicts the dissolution of compact planetary systems
3:00 PM4:00 PM April 14, 2021 Despite over three hundred years of effort, no solutions exist for predicting when a general planetary configuration will become unstable. I will discuss our deep learning architecture (arxiv:2101.04117) which pushes forward this problem for compact systems. While current machine learning algorithms in this area rely on scientistderived instability metrics, our new technique learns its own metrics from scratch, enabled by a novel internal structure inspired from dynamics theory. The Bayesian neural network model can accurately predict not only if, but also when a compact planetary system with three or more planets will go unstable. Our model, trained directly from short Nbody time series of raw orbital elements, is more than two orders of magnitude more accurate at predicting instability times than analytical estimators, while also reducing the bias of existing machine learning algorithms by nearly a factor of three. Despite being trained on threeplanet configurations, the model demonstrates robust generalization to fiveplanet systems, even outperforming models designed for that specific set of integrations. I will also discuss some work on recovering symbolic representations of such models using arxiv:2006.11287. Zoom: https://harvard.zoom.us/j/99018808011?pwd=SjRlbWFwVms5YVcwWURVN3R3S2tCUT09  NUMBER THEORY SEMINAR
3:00 PM4:00 PM April 14, 2021 We will describe the notion of affine schemes and their modifications in the context of Arakelov geometry. Using geometry of numbers in infinite rank, we will study their cohomological properties. Concretely, given an affine scheme X over Z and a compact subset K of the set of complex points of X, we will investigate the geometry of those proper arithmetic curves in X whose complex points lie in K. This is joint work with JeanBenoît Bost. Zoom: https://harvard.zoom.us/j/99334398740 Password: The order of the permutation group on 9 elements.
 15  CMSA EVENT: CMSA Interdisciplinary Science Seminar: Weak solutions to the isentropic system of gas dynamics
9:00 AM10:00 AM April 15, 2021 In this talk, I will discuss the global weak solutions to the isentropic system of gas dynamics: existence and nonuniqueness. In the first part, we generalized the renormalized techniques introduced by DiPernaLions to build up the global weak solutions to the compressible NavierStokes equations with degenerate viscosities. This existence result holds for any $\gamma>1$ in any dimensional spaces for the large initial data. In the second part, we proved that for any initial data belonging to a dense subset of the energy space, there exists infinitely many global weak solutions to the isentropic Euler equations for any $1<\gamma\leq 1+2/n$. Our result is based on a generalization of convex integration techniques by De LellisSzekelyhidi and weak vanishing viscosity limit of the NavierStokes equations. The first part is based on the joint works with D. Bresch and A. Vasseur, and the second one is based on our recent joint work with R. M Chen and A. Vasseur. Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09 (Password: 419419)  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: QCD without diagrams
10:30 AM12:00 PM April 15, 2021 QCD, the theory of the strong interactions, involves quarks interacting with nonAbelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about. Zoom: https://harvard.zoom.us/j/977347126  HARVARDMITBUBRANDEISNORTHEASTERN COLLOQUIUM
4:30 PM5:30 PM April 15, 2021
 16  CMSA EVENT: CMSA Math Science Literature Lecture Series
1:00 PM2:30 PM April 16, 2021 TITLE: Deep Networks from First Principles ABSTRACT: In this talk, we offer an entirely “white box’’ interpretation of deep (convolution) networks from the perspective of data compression (and group invariance). In particular, we show how modern deep layered architectures, linear (convolution) operators and nonlinear activations, and even all parameters can be derived from the principle of maximizing rate reduction (with group invariance). All layers, operators, and parameters of the network are explicitly constructed via forward propagation, instead of learned via back propagation. All components of soobtained network, called ReduNet, have precise optimization, geometric, and statistical interpretation. There are also several nice surprises from this principled approach: it reveals a fundamental tradeoff between invariance and sparsity for class separability; it reveals a fundamental connection between deep networks and Fourier transform for group invariance – the computational advantage in the spectral domain (why spiking neurons?); this approach also clarifies the mathematical role of forward propagation (optimization) and backward propagation (variation). In particular, the soobtained ReduNet is amenable to finetuning via both forward and backward (stochastic) propagation, both for optimizing the same objective. This is joint work with students Yaodong Yu, Ryan Chan, Haozhi Qi of Berkeley, Dr. Chong You now at Google Research, and Professor John Wright of Columbia University. Talk chair: Harry Shum 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.
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18  19  20  CMSA EVENT: CMSA Math Science Literature Lecture Series
9:00 AM10:30 AM April 20, 2021 TITLE: The AtiyahSinger Index Theorem ABSTRACT: The story of the index theorem ties together the Gang of Four— Atiyah, Bott, Hirzebruch, and Singer—and lies at the intersection of analysis, geometry, and topology. In the first part of the talk I will recount high points in the early developments. Then I turn to subsequent variations and applications. Throughout I emphasize the role of the Dirac operator. Talk chair: Cumrun Vafa 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.  MATHEMATICAL PICTURE LANGUAGE SEMINAR
10:00 AM11:00 AM April 20, 2021 Nuclear Magnetic Resonance (NMR) is a powerful spectroscopic technique that provides information about matter at an atomic resolution. One of the applications of NMR is to decipher the molecular architecture of biomolecules including nucleic acids and proteins. In addition to providing information on the structure of biomolecules, NMR also provides information on the dynamics of these molecule machines. The seminar will introduce some basics of NMR, discuss some of the current limitations, and present new methods to push the frontiers of NMR. Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09  CMSA EVENT: CMSA Computer Science for Mathematicians: EigenGame: SVD as a Nash Equilibrium
11:30 AM12:30 PM April 20, 2021 We present a novel view on singular value decomposition (SVD) as a competitive game in which each approximate singular vector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this EigenGame and the behavior of its gradient based updates. The resulting algorithm — which combines elements from Oja’s rule with a generalized GramSchmidt orthogonalization — is naturally decentralized and hence parallelizable through message passing. EigenGame’s updates are biased if computed using minibatches of data, which hinders convergence and more sophisticated parallelism in the stochastic setting. Therefore, in followup work, we propose an unbiased stochastic update that is asymptotically equivalent to EigenGame, enjoys greater parallelism allowing computation on datasets of larger sample sizes, and outperforms the original EigenGame in experiments. We demonstrate the a) scalability of the algorithm by conducting principal component analyses of large image datasets, language datasets, and neural network activations and b) generality by reusing the same algorithm to perform spectral clustering of a social network. We discuss how this new view of SVD as a differentiable game can lead to further algorithmic developments and insights. This talk is based on two recent works, both joint work with Brian McWilliams, Claire Vernade, and Thore Graepel — https://arxiv.org/abs/2010.00554 (EigenGame – ICLR ‘21) https://arxiv.org/abs/2102.04152 (EigenGame Unloaded – ICML ‘21 submission) — and will focus in detail on some of the more interesting mathematical properties of the game. Zoom: https://harvard.zoom.us/j/98231541450
 21  RANDOM MATRIX SEMINAR
2:00 PM3:00 PM April 21, 2021 Spin glasses are models of statistical mechanics encoding disordered interactions between many simple units. One of the fundamental quantities of interest is the free energy of the model, in the limit when the number of units tends to infinity. For a restricted class of models, this limit was predicted by Parisi, and later rigorously proved by Guerra and Talagrand. I will first show how to rephrase this result using an infinitedimensional HamiltonJacobi equation. I will then present partial results suggesting that this new point of view may allow to understand limit free energies for a larger class of models, focusing in particular on the case in which the units are organized over two layers, and only interact across layers. Zoom: https://harvard.zoom.us/j/99333938108  CMSA EVENT: CMSA New Technologies in Mathematics: Homotopy type theory and the quest for extensionality
3:00 PM4:00 PM April 21, 2021 Over the past decades, dependent type theory has proven to be a powerful framework for verified software and formalized mathematics. However, its treatment of equality has always been somewhat uncomfortable. Recently, homotopy type theory has made progress towards a more useful notion of equality, which natively implements both isomorphisminvariance in mathematics and representationindependence in programming. This progress is based on ideas from abstract homotopy theory and higher category theory, and with the development of cubical type theories it can be implemented as a true programming language. In this talk, I will survey these developments and their potential applications, and suggest some directions for further improvement. Zoom: https://harvard.zoom.us/j/99018808011?pwd=SjRlbWFwVms5YVcwWURVN3R3S2tCUT09  NUMBER THEORY SEMINAR
3:00 PM4:00 PM April 21, 2021
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