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PRODID:Mathematics Seminar Calendar
BEGIN:VEVENT
UID:20180318T133816-8242@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Elliptic curves and p-adic L-functions
DESCRIPTION:Speaker\: David Hansen, Columbia University\r\nI'll explain the notion of a p-adic L-function, try to \r\nmotivate why one might care about such a gadget, and give some history of their construction and applications. At the end of the talk I'll discuss a recent joint work with John Bergdall in which (among other things) we construct canonical p-adic L-functions associated with modular elliptic curves over totally real number fields.
LOCATION:C304 Wells Hall
DTSTART:20180108T211000Z
DTEND:20180108T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=8242
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BEGIN:VEVENT
UID:20180318T133816-8231@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Uncertainty Quantification of Physics-constrained Problems – Data Assimilation and Parameter Estimation
DESCRIPTION:Speaker\: Yoonsang Lee, Lawrence Berkeley National Laboratory\r\nObservation data along with mathematical models play a crucial role in improving prediction skills in science and engineering. In this talk we focus on the recent development of uncertainty quantification methods, data assimilation and parameter estimation, for Physics-constrained problems that are often described by partial differential equations. We discuss the similarities shared by the two methods and their differences in mathematical and computational points of view and future research topics. As applications, numerical weather prediction for geophysical flows and parameter estimation of kinetic reaction rates in the hydrogen-oxygen combustion are provided.
LOCATION:C304 Wells Hall
DTSTART:20180109T211000Z
DTEND:20180109T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=8231
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BEGIN:VEVENT
UID:20180318T133816-8230@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Quantifying congruences between Eisenstein series and cusp forms
DESCRIPTION:Speaker\: Preston Wake, UCLA\r\nConsider the following two problems in algebraic number theory:\r\n\r\n1. For which prime numbers p can we easily show that the Fermat equation x^p + y^p =z^p has no non-trivial integer solutions? \r\n\r\n\r\n2. Given an elliptic curve E over the rational numbers, what can be said about the group of rational points of finite order on E?\r\n\r\nThese seem like very different problems, but, surprisingly, they share a common theme: they are both related to the existence of congruences between two types of modular forms, Eisenstein series and cusp forms. We will explain these examples, and discuss a new technique for giving quantitative information about these congruences (for example, counting the number of cusp forms congruent to an Eisenstein series). We will explain how this can give finer arithmetic information than simply knowing the existence of a congruence. This is joint work with Carl Wang-Erickson.
LOCATION:C304 Wells Hall
DTSTART:20180110T211000Z
DTEND:20180110T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=8230
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BEGIN:VEVENT
UID:20180318T133816-8232@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:From Hilbert's Nullstellensatz to quotient categories
DESCRIPTION:Speaker\: John Calabrese, Rice University\r\nA common theme in algebraic geometry is the interplay between algebra and geometry. In this talk I will discuss a few "reconstruction theorems", in which the algebra determines the geometry.
LOCATION:C304 Wells Hall
DTSTART:20180112T211000Z
DTEND:20180112T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=8232
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BEGIN:VEVENT
UID:20180318T133816-9248@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Sasaki-Einstein metrics and K-stability
DESCRIPTION:Speaker\: Tristan Collins, Harvard University\r\nI will discuss the connection between Sasaki-Einstein metrics and algebraic geometry in the guise of K-stability. In particular, I will give a differential geometric perspective on K-stability which arises from the Sasakian view point, and use K-stability to find infinitely many non-isometric Sasaki-Einstein metrics on the 5-sphere. This is joint work with G. Szekelyhidi.
LOCATION:C304 Wells Hall
DTSTART:20180117T211000Z
DTEND:20180117T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9248
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BEGIN:VEVENT
UID:20180318T133816-9259@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Invariant and characteristic random subgroups and their applications
DESCRIPTION:Speaker\: Rostyslav Kravchenko, Northwestern University\r\nThe invariant random subgroups (IRS) were implicitly used by Stuck and Zimmer in 1994 and defined explicitly by Abert, Glasner and Virag in 2012. We recall the definition of IRS and discuss their properties. We also define the notion of characteristic random subgroups (CRS) which are a natural analog of IRSs for the case of the group of all automorphisms. We determine CRS for free abelian groups and for free groups of finite rank. Using our results on CRS of free groups we show that for some groups of geometrical nature there are infinitely many continuous ergodic IRS.
LOCATION:C304 Wells Hall
DTSTART:20180130T152000Z
DTEND:20180130T161000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9259
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BEGIN:VEVENT
UID:20180318T133816-9261@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Amenability of discrete groups and their actions
DESCRIPTION:Speaker\: Kate Juschenko, Northwestern University\r\nThe subject of amenability essentially begins in 1900's with Lebesgue. He asked whether the properties of his integral are really fundamental and follow from more familiar integral axioms. This led to the study of positive, finitely additive and translation invariant measure on reals as well as on other spaces. In particular the study of isometry-invariant measure led to the Banach-Tarski decomposition theorem in 1924. The class of amenable groups was introduced by von Neumann in 1929, who explained why the paradox appeared only in dimensions greater or equal to three, and does not happen when we would like to decompose the two-dimensional ball. In 1940's, M. Day formally defined a class of elementary amenable groups as the largest class of groups amenability of which was known to von Naumann. He asked whether there are other groups then that. Currently there are many groups that answer von Neumann-Day's question. However, in each particular case it is algebraically difficult to show that the group is not elementary amenable, and analytically difficult to show that it is amenable. The talk is aimed to discuss recent developments and approaches in the field. In particular, it will be shown how to prove amenability of all known non-elementary amenable groups using only one single approach. We will also discuss techniques coming from random walks of groups.
LOCATION:C304 Wells Hall
DTSTART:20180130T211000Z
DTEND:20180130T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9261
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BEGIN:VEVENT
UID:20180318T133816-9257@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Reaction-diffusion equations in biology
DESCRIPTION:Speaker\: Olga Turanova, UCLA\r\nReaction-diffusion equations describe a variety of physical and biological phenomena. In this talk, I begin by presenting the classical Fisher-KPP equation and its significance to ecology. I then describe recent results on other PDEs of reaction-diffusion type, including non-local equations arising in evolutionary ecology, as well as ones that model tumor growth (joint with Inwon Kim). I will highlight the mathematical challenges and techniques that arise in the analysis of these PDEs.
LOCATION:C304 Wells Hall
DTSTART:20180131T211000Z
DTEND:20180131T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9257
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BEGIN:VEVENT
UID:20180318T133816-9263@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Geodesic flow in non-positive curvature: An inspiration for new techniques in ergodic theory
DESCRIPTION:Speaker\: Daniel Thompson, Ohio State University\r\nWe discuss some recent progress in the smooth ergodic theory of geodesic flows. This talk will be suitable for a general mathematical audience, and will start with an intuitive overview of the classic results developed by luminaries such as Anosov, Bowen and Ruelle in the well understood setting of surfaces with variable negative curvature. Efforts to understand the much more difficult case of non-positive curvature were initiated by Pesin in the 1970’s. However, despite substantial successes, the picture has remained far from complete. There has been a great deal of recent progress in this area, which has required, and motivated, the development of new machinery in the abstract theory. I will give an overview of some recent developments, including:\r\n\r\n1) General machinery developed by Vaughn Climenhaga and myself, which gives “non-uniform" dynamical criteria for uniqueness of equilibrium measures;\r\n\r\n2) Joint work with Keith Burns, Vaughn Climenhaga and Todd Fisher, where we apply this machinery to geodesic flow on non-positive curvature manifolds;\r\n\r\n3) If time permits, I will also mention related joint work with Jean-Francois Lafont and Dave Constantine, where we develop the theory of equilibrium measures for geodesic flow on locally CAT(-1) spaces; these are geodesic metric spaces which generalize negative curvature Riemannian manifolds by having the “thin triangle” property.
LOCATION:C304 Wells Hall
DTSTART:20180201T211000Z
DTEND:20180201T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9263
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BEGIN:VEVENT
UID:20180318T133816-9265@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Quantum Integrable Systems and Enumerative Geometry
DESCRIPTION:Speaker\: Anton M. Zeitlin, Louisiana State University\r\nThe correspondence between integrable systems and enumerative geometry\r\nstarted roughly 25 years ago in the works of Givental and his collaborators,\r\nstudying quantum cohomology and quantum K-theory. Around 10 years ago,\r\nphysicists Nekrasov and Shatashvili proposed an unexpected relation between\r\nquantum K-theory and quantum integrable systems based on quantum groups\r\nwithin their studies of 3-dimensional gauge theories. Their bold proposal\r\nled to a lot of interesting developments in mathematics, bringing a new life\r\nto older ideas of Givental, and enriching it with flavors of geometric\r\nrepresentation theory via the results of Braverman, Maulik, Nakajima, Okounkov \r\nand many others. In this talk I will focus on recent breakthroughs in the\r\nsubject, leading to the proper mathematical understanding of Nekrasov-Shatashvili \r\noriginal papers as well as some other subsequent conjectures made by physicists. \r\nOur main illustration of such a relation is an interplay between equivariant quantum K-theory of the cotangent bundles to Grassmanians and the Heisenberg XXZ spin chain. We will also\r\ndiscuss relation of equivariant quantum K-theory of flag varieties and \r\nmany-body integrable systems of Ruijsenaars-Schneider and Toda.
LOCATION:C304 Wells Hall
DTSTART:20180205T211000Z
DTEND:20180205T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9265
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BEGIN:VEVENT
UID:20180318T133816-9266@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Optimal mixing and irregular transport by incompressible flows
DESCRIPTION:Speaker\: Anna Mazzucato, Pennsylvania State University\r\n I will discuss transport of passive scalars by incompressible flows (such as a die in a fluid) and measures of optimal mixing and stirring under physical constraint on the flow. In particular, I will present recent results concerning examples of flows that achieve the optimal theoretical rate in the case of flows with a prescribed bound on certain Sobolev norms of the associated velocity, such as under an energy or an enstrophy budget. These examples are related to examples of (instantaneous) loss of Sobolev regularity for solutions to linear transport equation with non-Lipschitz velocity.
LOCATION:C304 Wells Hall
DTSTART:20180209T211000Z
DTEND:20180209T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9266
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BEGIN:VEVENT
UID:20180318T133816-9270@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Spectral Optimization and Free Boundary Problems
DESCRIPTION:Speaker\: Dennis Kriventsov, NYU Courant\r\nA classic subject in analysis is the relationship between the spectrum of the Laplacian on a domain and that domain's geometry. One approach to understanding this relationship is to study domains which extremize some function of their spectrum under geometric constraints. I will explain how to attack these problems using tools from the calculus of variations to find solutions. A key difficulty with this method is showing that the optimizers (which are a priori very weak) are actually smooth domains, and I address this issue in some recent work with Fanghua Lin. Our results are based on relating spectral optimization problems to certain vector-valued free boundary problems of Bernoulli type.
LOCATION:C304 Wells Hall
DTSTART:20180212T211000Z
DTEND:20180212T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9270
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BEGIN:VEVENT
UID:20180318T133816-9271@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Non-tracial free transport
DESCRIPTION:Speaker\: Brent Nelson, UC Berkeley\r\nVon Neumann algebras are certain *-subalgebras of bounded operators acting on a Hilbert space. They are generally thought of as non-commutative measure spaces and offer connections to many fields of mathematics (e.g. group theory, low-dimensional topology, logic, ergodic theory, and random matrix theory to name a few). In some instances an analogy with probability spaces is more appropriate, and indeed this is precisely what informs the field of free probability, wherein one uses non-commutative analogs of probabilistic notions to study the structure of von Neumann algebras. One particular example of this is free transport. In probability theory, transport refers to a measurable map between probability spaces that pushes one measure onto the other. Following work of Brenier in 1991, transportation theory has known great success. Free transport, the non-commutative analog that was introduced by Guionnet and Shlyakhtenko in 2014, offers methods for proving isomorphisms between von Neumann algebras. In this talk, I will discuss these ideas as well my work, which used free transport to prove isomorphisms between certain so-called "non-tracial" von Neumann algebras.
LOCATION:C304 Wells Hall
DTSTART:20180216T211000Z
DTEND:20180216T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=9271
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BEGIN:VEVENT
UID:20180318T133816-11277@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Algorithms for mean curvature motion of networks
DESCRIPTION:Speaker\: Selim Esedoglu, University of Michigan\r\nMotion by mean curvature for networks of surfaces arises in a variety of\r\napplications, such as the dynamics of foam and the evolution of\r\nmicrostructure in polycrystalline materials. It is steepest descent\r\n(gradient flow) for an energy: the sum of the areas of the surfaces\r\nconstituting the network.\r\nDuring the evolution, surfaces may collide and junctions (where three or\r\nmore surfaces meet) may merge and split off in myriad ways as the\r\nnetwork coarsens in the process of decreasing its energy. The first idea\r\nthat comes to mind for simulating this evolution -- parametrizing the\r\nsurfaces and explicitly specifying rules for cutting and pasting when\r\ncollisions occur -- gets hopelessly complicated. Instead, one looks for\r\nalgorithms that generate the correct motion, including all the necessary\r\ntopological changes, indirectly but automatically via just a couple of\r\nsimple operations.\r\nAn almost miraculously elegant such algorithm, known as threshold\r\ndynamics, was proposed by Merriman, Bence, and Osher in 1992. Extending\r\nthis algorithm, while preserving its simplicity, to more general\r\nenergies where each surface in the network is measured by a different,\r\npossibly anisotropic, notion of area requires new mathematical\r\nunderstanding of the original version, which then elucidates a\r\nsystematic path to new algorithms.
LOCATION:C304 Wells Hall
DTSTART:20180301T211000Z
DTEND:20180301T220000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=11277
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BEGIN:VEVENT
UID:20180318T133816-13293@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Real applications of non-real numbers: Ramanujan graphs (First Phillips Lecture)
DESCRIPTION:Speaker\: Alex Lubotzky, Hebrew University\r\nThe real numbers form a completion of the field of rational numbers. We will describe the fields of p-adic numbers which are different completions of the rationals. Once they are defined, one can study analysis and geometry over them. While being very abstract, the main motivation for studying them came from number theory. Developments in the last 2-3 decades shows various applications to the real world: communication networks, etc. This is done via expander graphs and Ramanujna grpahs which are "Riemann surfaces over these p-adic fields". All notions will be explained.
LOCATION:
DTSTART:20180312T213000Z
DTEND:20180312T223000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=13293
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BEGIN:VEVENT
UID:20180318T133816-13295@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:High dimensional expanders: From Ramanujan graphs to Ramanujan complexes (Second Phillips Lecture)
DESCRIPTION:Speaker\: Alex Lubotzky, Hebrew University\r\nExpander graphs in general, and Ramanujan graphs, in particular, have played a major role in combinatorics and computer science in the last 4 decades and more recently also in pure math. Approximately 10 years ago, a theory of Ramanujan complexes was developed by Li, Lubotzky-Samuels-Vishne and others. In recent years a high dimensional theory of expanders is emerging. The notions of geometric and topological expanders were defined by Gromov in 2010 who proved that the complete d dimensional simplicial complexes are such. He raised the basic question of existence of such bounded degree complexes of dimension d greater than 1. Ramanujan complexes were shown to be geometric expanders by Fox-Gromov-Lafforgue-Naor-Pach in 2013, but it was left open if they are also topological expanders. By developing new isoperimetric methods for “locally minimal small” F_2-co-chains, it was shown recently by Kaufman- Kazdhan- Lubotzky for small dimensions and Evra-Kaufman for all dimensions that the d-skeletons of (d+1)-dimensional Ramanujan complexes provide bounded degree topological expanders. This answers Gromov’s original problem, but still leaves open whether the Ramanujan complexes themselves are topological expanders. We will describe these developments and the general area of high dimensional expanders and some of its open problems.
LOCATION:115 International Center
DTSTART:20180313T200000Z
DTEND:20180313T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=13295
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BEGIN:VEVENT
UID:20180318T133816-13296@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Groups' approximation, stability and high dimensional expanders (Third Phillips Lecture)
DESCRIPTION:Speaker\: Alex Lubotzky, Hebrew University\r\nSeveral well-known open questions (such as: are all groups sofic or hyperlinear?) have a common form: can all groups be approximated by asymptotic homomorphisms into the symmetric groups Sym(n) (in the sofic case) or the unitary groups U(n) (in the hyperlinear case)? \r\n\r\nIn the case of U(n), the question can be asked with respect to different metrics and norms. We answer, for the first time, one of these versions, showing that there exist fintely presented groups which are not approximated by U(n) with respect to the Frobenius (=L_2)norm. \r\n\r\nThe strategy is via the notion of “stability”: some higher dimensional cohomology vanishing phenomena is proven to imply stability and using higher dimensional expanders, it is shown that some non-residually finite groups (central extensions of some lattices in p-adic Lie groups) are Frobenious stable and hence cannot be Frobenius approximated. \r\n\r\nAll notions will be explained. Joint work with M. De Chiffre, L. Glebsky and A. Thom.
LOCATION:C304 Wells Hall
DTSTART:20180314T140000Z
DTEND:20180314T150000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=13296
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BEGIN:VEVENT
UID:20180318T133816-13288@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:Number theory in geometry
DESCRIPTION:Speaker\: Gopal Prasad, University of Michigan\r\nHistorically, it is geometry which led to important developments in several areas of mathematics including number theory. But recently there have been several instances of number theory being applied to settle important questions in geometry. I will talk about two problems in whose solution number theory has been used in a crucial way. \r\n\r\nThe first one, settled in collaboration with Sai-Kee Yeung, is classification of fake projective planes and their higher dimensional analogs. (I recall that fake projective planes are smooth projective complex surfaces with same Betti numbers as the complex projective plane, but which are not isomorphic to the complex projective plane. The first such surface was constructed by David Mumford.) \r\n\r\nThe second problem concerns compact Riemannian manifolds and it has the following very interesting formulation due to Mark Kac: “Can one hear the shape of a drum?”. In precise mathematical terms, the question asks whether two compact Riemannian manifolds with same spectrum (i.e., the set of eigenvalues counted with multiplicities) are isometric. The answer is in general “no”. However, Andrei Rapinchuk and I investigated Kac’s question, using number theoretic results and tools, for a particularly nice class of manifolds, namely locally symmetric spaces. The answer turned out to be very interesting and has led to several other developments which, if time permits, I will mention.
LOCATION:C304 Wells Hall
DTSTART:20180405T201000Z
DTEND:20180405T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=13288
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UID:20180318T133816-13289@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Maria Gualdani, George Washington University\r\n
LOCATION:C304 Wells Hall
DTSTART:20180412T201000Z
DTEND:20180412T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=13289
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BEGIN:VEVENT
UID:20180318T133816-13290@math.msu.edu
DTSTAMP:20180318T133816Z
SUMMARY:TBA
DESCRIPTION:Speaker\: Zinovy Reichstein, University of British Columbia\r\n
LOCATION:C304 Wells Hall
DTSTART:20180419T201000Z
DTEND:20180419T210000Z
URL:https://math.msu.edu/Seminars/TalkView.aspx?talk=13290
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