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October 2021

Nishant Chandgotia, Tata institute in India – Ergodic Theory Seminar

October 27, 2021 @ 3:00 pm - 4:00 pm

Mode: Zoom Title: About Borel and almost Borel embeddings for ZD actions Abstract:Krieger's generator theorem says that all free ergodic measure preserving actions (under natural entropy constraints) can be modelled by a full shift. Following results by Anush Tserunyan and answering a question by Benjamin Weiss, in a sequence of two papers Mike Hochman noticed that this theorem can be strengthened: He showed that all free homeomorphisms of a Polish space (under entropy constraints) can be Borel embedded into the…

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November 2021

Professor Andrew Torok, University of Houston – Ergodic Theory Seminar

November 17, 2021 @ 12:00 pm - 1:00 pm

Time: 12:10 - 1:10 pm Mode: Zoom Title: Stable laws for random dynamical systems. Abstract: For a random system consisting of beta-transformations, or more general uniformly expanding maps, we consider the convergence to a stable law (the analogue of the Central Limit Theorem for certain observations that have infinite second moments). We obtain quenched convergence (that is, for almost each choice of the sequence of maps) in the Skorokhod J_1 topology, by extending results of Marta Tyran-Kaminska. This is joint work…

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Dima Arinkin, University of Wisconsin, Madison – Mathematics Colloquium

November 18, 2021 @ 4:00 pm - 5:00 pm

Mode: Zoom Title: Moduli spaces and their compactifications Abstract: Very broadly speaking, geometry is the study of spaces. Here `space' is a  placeholder: different flavors of geometry work with spaces such as differentiable manifolds (differential geometry), topological spaces (topology), varieties (algebraic geometry, my favorite), and so on. But what makes a space an interesting object of study? One class of `interesting' spaces is the so-called moduli spaces (the word `moduli' goes back to Riemann and means `parameters'). Moduli spaces parametrize objects of…

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January 2022

Prakash Belkale, UNC-CH – Geometric Methods in Representation Theory Seminar

January 21 @ 4:00 pm - 5:00 pm

Mode: Zoom only! Title: Rigid local systems and the multiplicative eigenvalue problem Abstract: Local systems are sheaves which describe the behavior of solutions of differential equations. A local system is rigid if local monodromy determines global monodromy. We give a construction which produces irreducible complex rigid local systems on a punctured Riemann sphere via quantum Schubert calculus and strange duality. These local systems are unitary and arise from a study of vertices in the polytopes controlling the multiplicative eigenvalue problem for the…

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Sung-Jin Oh, UC Berkeley – Analysis & PDE Seminar

January 26 @ 2:30 pm - 3:30 pm

Mode: Zoom only Title: A tale of two tails Abstract: In this talk, I will introduce a general method for understanding the late-time tail for solutions to wave equations on asymptotically flat spacetimes with odd spatial dimensions. A particular consequence of the method is a re-proof of Price’s law-type results, which concern the sharp decay rate of the late-time tails on stationary spacetimes. Moreover, the method also applies to dynamical spacetimes. In this case, I will explain how the late-time tails are…

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February 2022

Lisa Piccirillo, MIT – Mathematics Colloquium

February 10 @ 4:00 pm - 5:00 pm

Mode: Zoom only Virtual tea at 3:45pm Title: Knot concordance and 4-manifolds Abstract: There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will describe a weak notion of equivalence for knots called concordance, and highlight some historical and recent connections between knot concordance and the study of 4-manifolds, with a particular emphasis on applications of knot concordance to the construction and detection of small 4-manifolds which admit multiple smooth…

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Cristian Lenart, SUNY Albany – Geometric Methods in Representation Theory Seminar

February 11 @ 4:00 pm - 5:00 pm

Mode: Zoom only Title: A combinatorial Chevalley formula for semi-infinite flag manifolds and related topics Abstract: I present a combinatorial Chevalley formula for an arbitrary weight in the equivariant K-theory of semi-infinite flag manifolds, which are certain affine versions of finite flag manifolds G/B. The formula is expressed in terms of the so-called quantum alcove model. One application is a Chevalley formula in the equivariant quantum K-theory of G/B. Another application is that the so-called quantum Grothendieck polynomials represent Schubert…

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Ken Ono – Mathematics Colloquium Talk

February 24 @ 4:00 pm - 5:00 pm

Mode: Virtual only Virtual Tea-time at 3:45 pm Title: New results in arithmetic statistics Abstract:  Studying the statistical behavior of number theoretic quantities is presently in vogue. This lecture will begin with a new look at classical results in number theory from the perspective of arithmetic statistics, which then naturally lead to point counts for elliptic curves and K3 surfaces over finite fields. This lecture will use the celebrated Sato-Tate Conjecture (now theorem thanks to Richard Taylor and his collaborators) as motivation…

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March 2022

Aidan Young, UNC-CH – Ergodic Theory Seminar

March 1 @ 4:00 pm - 5:00 pm

Speaker: Aidan Young Title: Spatial-Temporal Differentiation Theorems Abstract: We present a type of ergodic-theoretic differentiation problem that synthesizes spatial and temporal differentiation problems, creatively termed a spatial-temporal differentiation problem. We describe the problem, and present various convergence results. We also describe a generalization of the problem to non-autonomous dynamical systems. Based on joint work with Idris Assani. Time: Tuesday, March 1st, 4pm Mode: Zoom

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April 2022

Xueying Yu – Analysis & PDE Seminar

April 5 @ 4:00 pm - 5:00 pm

Mode: Zoom only, please note the different day! Title: Global well-posedness for the fractional NLS on the unit disk Abstract: In this talk, we discuss the cubic nonlinear Schrodinger equation with the fractional Laplacian on the unit disk. We show global well-posedness for certain radial initial data below the energy space and establish a polynomial bound of the global solution. The result is proved by extending the I-method to the fractional nonlinear Schrodinger equation setting.

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Tamas Hausel, IST Austria – Mathematics Colloquium

April 7 @ 2:00 pm - 3:00 pm

Time: Thursday, April 7th, 2:00 pm - 3:00 pm Mode: Zoom Title: Ubiquity of systems of homogenous polynomial equations with a unique solution Abstract: Following Macaulay we will analyse systems of equations as in the title leading to marvelous properties of its multiplicity algebra. Examples include isolated surface singularities, equivariant cohomology and fixed point sets of group actions as well as the Hitchin integrable system on very stable upward flows.  

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Dinakar Muthiah, Glasgow – Geometric Methods in Representation Theory Seminar

April 22 @ 4:00 pm - 5:00 pm

Mode: Zoom Title: Fundamental monopole operators and affine Grassmannian slices Abstract: Affine Grassmannians are objects of central interest in geometric representation theory. For example, the geometric Satake correspondence tells us that their singularities carry representation theoretic information. In fact, it suffices to work with affine Grassmannian slices, which retain all of this information. Recently, Braverman, Finkelberg, and Nakajima showed that affine Grassmannian slices arise as Coulomb branches of certain quiver gauge theories. Remarkably, their construction works in Kac-Moody type as…

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