news

See Older News

announcements

upcoming events

< 2020 >
November
«
»
Sun
Mon
Tue
Wed
Thu
Fri
Sat
1
2
  • CMSA EVENT: CMSA Mathematical Physics Seminar: Double-Janus linear sigma models and generalized quadratic reciprocity
    10:30 AM-11:30 AM
    November 2, 2020

    We study the supersymmetric partition function of a 2d linear sigma-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d N=4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T^2 fibered over S^1) times a circle with an SL(2,Z) duality wall inserted on S^1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2,Z), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.

    Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09

3
  • MATHEMATICAL PICTURE LANGUAGE SEMINAR
    10:00 AM-11:00 AM
    November 3, 2020

    In this talk, I present recent joint work with Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang and Hao Zheng (arXiv:2003.08898). We propose a mathematical theory of symmetry protected trivial (SPT) order, and of anomaly-free symmetry enriched topological (SET) order in all dimensions. We employ two different approaches (with an emphasis on the second one). Our first approach relies on gauging the symmetry. Our second approach relies on a boundary-bulk relation. We conjecture the equivalence of these two approaches, yielding a number of interesting mathematical conjectures. 

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • MATHEMATICAL PICTURE LANGUAGE SEMINAR
    10:00 AM-11:00 AM
    November 3, 2020

    In this talk, I present recent joint work with Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang and Hao Zheng (arXiv:2003.08898). We propose a mathematical theory of symmetry protected trivial (SPT) order, and of anomaly-free symmetry enriched topological (SET) order in all dimensions. We employ two different approaches (with an emphasis on the second one). Our first approach relies on gauging the symmetry. Our second approach relies on a boundary-bulk relation. We conjecture the equivalence of these two approaches, yielding a number of interesting mathematical conjectures. 

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • CMSA EVENT: CMSA Computer Science for Mathematicians: Fast and Accurate Least-Mean-Squares Solvers
    11:30 AM-12:30 PM
    November 3, 2020

    Least-mean squares (LMS) solvers such as Linear / Ridge / Lasso-Regression, SVD and Elastic-Net not only solve fundamental machine learning problems, but are also the building blocks in a variety of other methods, such as decision trees and matrix factorizations.

    We suggest an algorithm that gets a finite set of $n$ $d$-dimensional real vectors and returns a weighted subset of $d + 1$ vectors whose sum is exactly the same. The proof in Caratheodory’s Theorem (1907) computes such a subset in $O(n^2 d^2 )$ time and thus not used in practice. Our algorithm computes this subset in $O(nd)$ time, using $O(logn)$ calls to Caratheodory’s construction on small but “smart” subsets. This is based on a novel paradigm of fusion between different data summarization techniques, known as sketches and coresets.

    As an example application, we show how it can be used to boost the performance of existing LMS solvers, such as those in scikit-learn library, up to $x100$. Generalization for streaming and distributed (big) data is trivial. Extensive experimental results and complete open source code are also provided.

    Zoom: https://harvard.zoom.us/j/98231541450

  • HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR
    3:00 PM-4:00 PM
    November 3, 2020

    Determining the computational complexity of matrix multiplication has been one of the central open problems in theoretical computer science ever since in 1969 Strassen presented an algorithm for multiplication of n by n matrices requiring only O(n^2.81) arithmetic operations. I will briefly discuss this problem and its reduction to deciding on which secant variety to the Segre embedding of a product of three projective spaces the matrix multiplication tensor lies. I will explain a recent technique to rule out membership of a fixed tensor in such secant varieties, border apolarity. Border apolarity establishes the existence of certain multigraded ideals implied by membership in a particular secant variety. These ideals may be assumed to be fixed under a Borel subgroup of the group of symmetries of the tensor, and in the simplest case, can consequently be tractably shown not to exist. When ideals exist satisfying the easily checkable properties, one must decide if they are limits of ideals of distinct points on the Segre. This talk discusses joint work with JM Landsberg, Alicia Harper, and Amy Huang.

    Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09

4
5
  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: The information bottleneck: A numerical microscope for order parameters
    10:30 AM-12:00 PM
    November 5, 2020

    The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.

    Zoom: https://harvard.zoom.us/j/977347126

  • COLLOQUIUMS
    4:30 PM-5:30 PM
    November 5, 2020

    Lacunary trigonometric sums are known to exhibit several properties that are typical of sums of iid random variables such as the central limit theorem, established by Salem and Zygmund, and the law of the iterated logarithm, due to Erdos and Gal.  We initiate an investigation of large deviation principles for such sums, and show that they display several interesting features, including sensitivity to the arithmetic properties of the corresponding lacunary sequence.  This is joint work with C. Aistleitner, N. Gantert, Z. Kabluchko and J. Prochno.

    Zoom: https://brandeis.zoom.us/j/93794552542

6
  • CMSA EVENT: CMSA Strongly Correlated Quantum Materials and High-Temperature Superconductors Series: Essential Ingredients for Superconductivity in Cupper Oxide Superconductors
    12:30 PM-2:00 PM
    November 6, 2020

    High‐temperature superconductivity in cupper oxides, with critical temperature well above what was anticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond. Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.

    [1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003)
    [2] M. Hashimoto et al., Nature Physics 10, 483 (2014)
    [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys.
    [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993)
    [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995)
    [6] A. Lanzara et al., Nature 412, 510 (2001)
    [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004)
    [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004)
    [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995)
    [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996)
    [11] A.G. Loeser et al., Science 273, 325 (1996)
    [12] S. Chen et al., Science, 366, 6469 (2019)
    [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004)
    [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012)
    [15] Yu He et al., Science, 362, 62 (Oct. 2018)
    [16] Z. Chen, Y. Wang et al., preprint, 2020

    Zoom: https://harvard.zoom.us/j/977347126

7
8
9
10
  • MATHEMATICAL PICTURE LANGUAGE SEMINAR

    MATHEMATICAL PICTURE LANGUAGE SEMINAR
    Learning to Unknot

    10:00 AM-11:00 AM
    November 10, 2020

    How does a child learn to speak, without prior direct communication, nor with having dictionary to translate words from another language? How do we learn to play chess, with no prior intuition about a myriad of different positions on the board nor with tactics to achieve those positions? How do scientists manage to move into the unknown, with no one guiding them through the right steps? And, how do they discover the previously unknown “right steps,” tools, and techniques in the first place? Curiously, there are many questions like these, which we face on a day-to-day basis and to which we have no good answers. Yet, we all find ways to make progress. How is it possible? We will take a look at this magic process by putting the smooth 4-dimensional Poincaré conjecture into the framework of Natural Language Processing (NLP).

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR
    10:00 AM-11:00 AM
    November 10, 2020

    Given a variation of Hodge structures $V$ on a smooth complex quasi-projective variety $S$, its Hodge locus is the set of points $s$ in $S$ where the Hodge structure $V_s$ admits exceptional Hodge tensors. A famous result of Cattani, Deligne and Kaplan shows that this Hodge locus is a countable union of irreducible algebraic subvarieties of $S$, called the special subvarieties of $(S, V)$. In this talk I will discuss the geometry of the Zariski closure of the union of the positive dimensional special subvarieties. This is joint work with Ania Otwinowska.

    Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09

  • MATHEMATICAL PICTURE LANGUAGE SEMINAR

    MATHEMATICAL PICTURE LANGUAGE SEMINAR
    Learning to Unknot

    10:00 AM-11:00 AM
    November 10, 2020

    How does a child learn to speak, without prior direct communication, nor with having dictionary to translate words from another language? How do we learn to play chess, with no prior intuition about a myriad of different positions on the board nor with tactics to achieve those positions? How do scientists manage to move into the unknown, with no one guiding them through the right steps? And, how do they discover the previously unknown “right steps,” tools, and techniques in the first place? Curiously, there are many questions like these, which we face on a day-to-day basis and to which we have no good answers. Yet, we all find ways to make progress. How is it possible? We will take a look at this magic process by putting the smooth 4-dimensional Poincaré conjecture into the framework of Natural Language Processing (NLP).

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • CMSA EVENT: CMSA Computer Science for Mathematicians: Graph Neural Networks: Expressive Power, Generalization, and Extrapolation
    11:30 AM-12:30 PM
    November 10, 2020

    Recent advances in deep learning exploit the structure in data and architectures. Graph Neural Network (GNN) is a powerful framework for learning with graph-structured objects, and for learning the interaction of objects on a graph. Applications include recommender systems, drug discovery, physical and visual reasoning, program synthesis, and natural language processing.

    In this talk, we study GNNs from the following aspects: expressive power, generalization, and extrapolation. We characterize the expressive power of GNNs from the perspective of graph isomorphism tests. We show an upper bound that GNNs are at most as powerful as a Weisfeiler-Lehman test. We then show conditions to achieve this upper bound, and present a maximally powerful GNN. Next, we analyze the generalization of GNNs. The optimization trajectories of over-parameterized GNNs trained by gradient descent correspond to those of kernel regression using a specific graph neural tangent kernel. Using this relation, we show GNNs provably learn a class of functions on graphs. More generally, we study how the architectural inductive biases influence generalization in a task. We introduce an algorithmic alignment measure, and show better alignment implies better generalization. Our framework suggests GNNs can sample-efficiently learn dynamic programming algorithms. Finally, we study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution (e.g., on larger graphs or edge weights). We prove a linear extrapolation behavior of ReLU multilayer perceptrons (MLPs), and identify conditions under which MLPs and GNNs extrapolate well. Our results suggest how a good representation or architecture can help extrapolation.

    Talk based on:
    https://arxiv.org/abs/1810.00826 
    ICLR’19 (oral)
    https://arxiv.org/abs/1905.13192 
    NeurIPS’19
    https://arxiv.org/abs/1905.13211 
    ICLR’20 (spotlight)
    https://arxiv.org/abs/2009.11848 

    Zoom: https://harvard.zoom.us/j/98231541450

  • DIFFERENTIAL GEOMETRY SEMINAR
    8:00 PM-9:00 PM
    November 10, 2020

    The 2D Toda system consists of a complicated set of infinitely many coupled PDEs in infinitely many variables that is known to assemble into an infinite-dimensional integrable system. Krichever and Zabrodin made the remarkable observation that the poles of some special meromorphic solutions to the 2D Toda system are known to evolve in time according to the Ruijsenaars-Schneider many particle integrable system. In this talk I will describe work in progress to establish this 2D Toda-RS correspondence via a Fourier-Mukai equivalence of derived categories: a category of “RS spectral sheaves” on one side, and a category of “Toda micro-difference operators” on another. This description of the 2D Toda-RS correspondence mirrors that of the KP-CM corrspondence previously established by two of the authors and suggests the existence of a conjectural elliptic integrable hierarchy.

    Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

11
  • CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Aspects of fermionic SPT phases: boundary supersymmetry and unwinding
    10:30 AM-12:00 PM
    November 11, 2020

    Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.

    Zoom: https://harvard.zoom.us/j/977347126

  • NUMBER THEORY SEMINAR
    3:00 PM-4:00 PM
    November 11, 2020

    For a smooth proper (formal) scheme X defined over a valuation ring of mixed characteristic, the crystalline cohomology H of its special fiber has the structure of an F-crystal, to which one can attach a Newton polygon and a Hodge polygon that describe the ”slopes of the Frobenius action on H”. The shape of these polygons are constrained by the geometry of X — in particular by the Hodge numbers of both the special fiber and the generic fiber of X. One instance of such constraints is given by a beautiful conjecture of Katz (now a theorem of Mazur, Ogus, Nygaard etc.), another constraint comes from the notion of “weakly admissible” Galois representations.

    In this talk, I will discuss some results regarding the shape of the Frobenius action on the F-crystal H and the Hodge numbers of the generic fiber of X, along with generalizations in several directions. In particular, we give a new proof of the fact that the Newton polygon of the special fiber of X lies on or above the Hodge polygon of its generic fiber, without appealing to Galois representations. A new ingredient that appears is (a generalized version of) the Nygaard filtration of the prismatic/Ainf cohomology, developed by Bhatt, Morrow and Scholze.

    Zoom: https://harvard.zoom.us/j/96767001802

    Password: The order of the permutation group on 9 elements.

  • CMSA EVENT: CMSA New Technologies in Mathematics: Towards AI for mathematical modeling of complex biological systems: Machine-learned model reduction, spatial graph dynamics, and symbolic mathematics
    3:00 PM-4:00 PM
    November 11, 2020

    The complexity of biological systems (among others) makes demands on the complexity of the mathematical modeling enterprise that could be satisfied with mathematical artificial 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.

    Zoom: https://harvard.zoom.us/j/96047767096?pwd=M2djQW5wck9pY25TYmZ1T1RSVk5MZz09

  • RANDOM MATRIX SEMINAR
    3:00 PM-4:00 PM
    November 11, 2020

    We consider eigenvector statistics of large symmetric random matrices. When the matrix entries are sampled from independent Gaussian random variables, eigenvectors are uniformly distributed on the sphere and numerous properties can be computed exactly. In particular, we can bound their extremal coordinates with high probability. There has been an extensive amount of work on generalizing such a result, known as delocalization, to more general entry distributions. After giving a brief overview of the previous results going in this direction, we present an optimal delocalization result for matrices with sub-exponential entries for all eigenvectors. The proof is based on the dynamical method introduced by Erdos-Yau, an analysis of high moments of eigenvectors as well as new level repulsion estimates which will be presented during the talk. This is based on a joint work with P. Lopatto.

    via Zoom: https://harvard.zoom.us/j/98520388668

12
13
14
15
16
  • CMSA EVENT: CMSA Math Science Literature Lecture Series
    8:00 AM-9:30 AM
    November 16, 2020

    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 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

    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.

    Register here to attend.
  • CMSA EVENT: CMSA Mathematical Physics Seminar: Differential equations and mixed Hodge structures
    10:00 AM-11:00 AM
    November 16, 2020

    We report on a new development in asymptotic Hodge theory, arising from work of Golyshev–Zagier and Bloch–Vlasenko, and connected to the Gamma Conjectures in Fano/LG-model mirror symmetry. The talk will focus exclusively on the Hodge/period-theoretic aspects through two main examples. Given a variation of Hodge structure M on a Zariski open in P^1, the periods of the limiting mixed Hodge structures at the punctures are interesting invariants of M.  More generally, one can try to compute these asymptotic invariants for iterated extensions of M by “Tate objects”, which may arise for example from normal functions associated to algebraic cycles. The main point of the talk will be that (with suitable assumptions on M) these invariants are encoded in an entire function called the motivic Gamma function, which is determined by the Picard-Fuchs operator L underlying M. In particular, when L is hypergeometric, this is easy to compute and we get a closed-form answer (and a limiting motive).  In the non-hypergeometric setting, it yields predictions for special values of normal functions; this part of the story is joint with V. Golyshev and T. Sasaki.

    Zoom: https://harvard.zoom.us/j/91780604388?pwd=d3BqazFwbDZLQng0cEREclFqWkN4UT09

17
  • MATHEMATICAL PICTURE LANGUAGE SEMINAR
    10:00 AM-11:00 AM
    November 17, 2020

    Consider a free group and its group von Neumann algebra A. Finding
    criteria on the boundedness or complete boundedness of multipliers on the Lp(A) is a major subject of analysis on free groups. A remarkable result of U↵e Haagerup and his co-authors characterizes the completely bounded radial Fourier multipliers on A (i.e., for p = 1). However, the case of finite p 6= 2 is a considerably more delicate matter, as it is for abelian groups. One of very few existing significant results is that on the free Hilbert transform recently proved by Tao Mei and Eric Ricard. In this talk I will present some new work, joint with these authors. A more-detailed abstract can be found in the seminar announcement at https://mathpicture.fas.harvard.edu/seminar.

    Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

  • CMSA EVENT: CMSA Computer Science for Mathematicians: Differentially Private Simple Linear Regression
    11:30 AM-12:30 PM
    November 17, 2020

    Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets of the data. Unfortunately, such fine-grained analysis can easily reveal sensitive individual information. We study algorithms for simple linear regression that satisfy differential privacy, a constraint which guarantees that an algorithm’s output reveals little about any individual input data record, even to an attacker with arbitrary side information about the dataset. We consider the design of differentially private algorithms for simple linear regression for small datasets, with tens to hundreds of datapoints, which is a particularly challenging regime for differential privacy. Focusing on a particular application to small-area analysis in economics research, we study the performance of a spectrum of algorithms we adapt to the setting. We identify key factors that affect their performance, showing through a range of experiments that algorithms based on robust estimators (in particular, the Theil-Sen estimator) perform well on the smallest datasets, but that other more standard algorithms do better as the dataset size increases. See https://arxiv.org/abs/2007.05157 for more details.

    Joint work with Audra McMillan, Jayshree Sarathy, Adam Smith, and Salil Vadhan.

    If time permits, I will chronicle past work on differentially private linear regression, discussing previous works on distributed linear regression and hypothesis testing in the general linear model.

    Zoom: https://harvard.zoom.us/j/98231541450

  • HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR

    HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR
    Top weight cohomology of A_g

    3:00 PM-4:00 PM
    November 17, 2020

    I will discuss recent work on computing the top weight cohomology of A_g for g up to 7. We use combinatorial methods coming from the relationship between the top weight cohomology of A_g and the homology of the link of the moduli space of tropical abelian varieties to carry out the computation. This is joint work with Madeline Brandt, Juliette Bruce, Melody Chan, Margarida Melo, and Corey Wolfe.

    Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09

  • DIFFERENTIAL GEOMETRY SEMINAR
    8:00 PM-9:00 PM
    November 17, 2020

    I will discuss the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibration structure, when the Kahler class degenerates to the pullback of a Kahler class from the base. I will present recent work with Hans-Joachim Hein where we obtain a priori estimates of all orders for the Ricci-flat metrics away from the singular fibers, as a corollary of a complete asymptotic expansion.

    Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

18
19
20
  • CMSA EVENT: CMSA Math Science Literature Lecture Series
    8:00 AM-9:30 AM
    November 20, 2020

    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 sands 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 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

    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.

    Register here to attend.
21
22
23
24
  • CMSA EVENT: CMSA Computer Science for Mathematicians: Large-scale multi-robot systems: From algorithmic foundations to smart-mobility applications
    11:30 AM-12:30 PM
    November 24, 2020

    Multi-robot systems are already playing a crucial role in manufacturing, warehouse automation, and natural resource monitoring, and in the future they will be employed in even broader domains from space exploration to search-and-rescue. Moreover, these systems will likely be incorporated in our daily lives through drone delivery services and smart mobility systems that comprise of thousands of autonomous vehicles. The anticipated benefits of multi-robot systems are numerous, ranging from automating dangerous jobs, to broader societal facets such  as easing traffic congestion and sustainability. However, to reap those rewards we must develop control mechanisms for such systems that can adapt rapidly to unexpected changes on a massive scale. Importantly, these mechanisms must capture: (i) dynamical and collision-avoidance constraints of individual robots; (ii) interactions between multiple robots; and (iii) more broadly, the  interaction of those systems with the environment. All these considerations give rise to extremely complex and high-dimensional optimization problems that need to be solved in real-time.

    In this talk I will present recent progress on the design of algorithms for  control and decision-making to allow the safe, effective, and societally-equitable deployment of multi-robot systems. I will highlight both results on fundamental capabilities for multi-robot systems (e.g., motion planning and task allocation), as well as applications in smart mobility, including multi-drone delivery and autonomous mobility-on-demand systems. Along the way, I will mention a few related open problems in mathematics and algorithm design.

    BIO:
    Kiril Solovey is roboticist specializing in multi-robot systems and their applications to smart mobility. He is currently a Postdoctoral Scholar at the Department of Aeronautics and Astronautics, Stanford University, working with Marco Pavone, where he is supported by the Center for Automotive Research (CARS). He obtained a PhD in Computer Science from Tel Aviv University, where he was advised by Dan Halperin.

    Kiril’s research focuses on the design of effective control and decision-making mechanisms to allow multi-robot systems to tackle complex problems for the benefit of the society. His work draws upon ideas that span across the disciplines of engineering, computer science, and transportation science, to develop scalable optimization approaches with substantial guarantees regarding quality and robustness of the solution. For his work he received multiple awards, including the Clore Scholars and Fulbright Postdoctoral Fellowships, best paper awards and nominations (at Robotics: Science and Systems, International Conference on Robotics and Automation, International Symposium on Multi-Robot and Multi-Agent System, and European Control Conference), and teaching awards.

    Zoom: https://harvard.zoom.us/j/98231541450

  • CMSA EVENT: CMSA Computer Science for Mathematicians: Large-scale multi-robot systems: From algorithmic foundations to smart-mobility applications
    11:30 AM-12:30 PM
    November 24, 2020

    Multi-robot systems are already playing a crucial role in manufacturing, warehouse automation, and natural resource monitoring, and in the future they will be employed in even broader domains from space exploration to search-and-rescue. Moreover, these systems will likely be incorporated in our daily lives through drone delivery services and smart mobility systems that comprise of thousands of autonomous vehicles. The anticipated benefits of multi-robot systems are numerous, ranging from automating dangerous jobs, to broader societal facets such  as easing traffic congestion and sustainability. However, to reap those rewards we must develop control mechanisms for such systems that can adapt rapidly to unexpected changes on a massive scale. Importantly, these mechanisms must capture: (i) dynamical and collision-avoidance constraints of individual robots; (ii) interactions between multiple robots; and (iii) more broadly, the  interaction of those systems with the environment. All these considerations give rise to extremely complex and high-dimensional optimization problems that need to be solved in real-time.

    In this talk I will present recent progress on the design of algorithms for  control and decision-making to allow the safe, effective, and societally-equitable deployment of multi-robot systems. I will highlight both results on fundamental capabilities for multi-robot systems (e.g., motion planning and task allocation), as well as applications in smart mobility, including multi-drone delivery and autonomous mobility-on-demand systems. Along the way, I will mention a few related open problems in mathematics and algorithm design.

    BIO:
    Kiril Solovey is roboticist specializing in multi-robot systems and their applications to smart mobility. He is currently a Postdoctoral Scholar at the Department of Aeronautics and Astronautics, Stanford University, working with Marco Pavone, where he is supported by the Center for Automotive Research (CARS). He obtained a PhD in Computer Science from Tel Aviv University, where he was advised by Dan Halperin.

    Kiril’s research focuses on the design of effective control and decision-making mechanisms to allow multi-robot systems to tackle complex problems for the benefit of the society. His work draws upon ideas that span across the disciplines of engineering, computer science, and transportation science, to develop scalable optimization approaches with substantial guarantees regarding quality and robustness of the solution. For his work he received multiple awards, including the Clore Scholars and Fulbright Postdoctoral Fellowships, best paper awards and nominations (at Robotics: Science and Systems, International Conference on Robotics and Automation, International Symposium on Multi-Robot and Multi-Agent System, and European Control Conference), and teaching awards.

    Zoom: https://harvard.zoom.us/j/98231541450

  • DIFFERENTIAL GEOMETRY SEMINAR

    DIFFERENTIAL GEOMETRY SEMINAR
    Metric SYZ conjecture

    8:00 PM-9:00 PM
    November 24, 2020

    One possible interpretation of the SYZ conjecture is that for a polarized family of CY manifolds near the large complex structure limit, there is a special Lagrangian fibration on the generic region of the CY manifold. Generic here means a set with a large percentage of the CY measure, and the percentage tends to 100% in the limit. I will discuss my recent progress on this version of the SYZ conjecture, with emphasis on how differential geometers think about this problem, and give some hint about where nonarchimedean geometry comes in.

    Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

25
26
27
28
29
30
December
December
December
December
December