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1 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Botong Wang (University of Wisconsin (Madison)) "The Hodge theory of hyperplane arrangements and matroids" Time: 15:30 Room: Zoom Given a hyperplane arrangement, we associate two projective varieties: the wonderful compactification and the matroid Schubert variety. Adiprasito, Huh and Katz used the Hodge-Riemann relations of the wonderful compactification (and their combinatorial generalizations) to prove that the coefficients of their characteristic polynomials form a log-concave sequence. In a joint work with Huh, we proved Dowling and Wilson's Top-heavy conjecture for realizable matroids by applying the hard Lefschetz theorem to the matroid Schubert varieties. In a more recent work with Braden, Huh, Matherne and Proudfoot, we proved the Top-heavy conjecture to arbitrary matroids. In this talk, I will go over some of the key ideas about the proof of the Top-heavy conjectures. If time permits, I will also mention some on-going works with my students Colin Crowley and Connor Simpson towards generalizations to type A Coxeter matroids.
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3 Geometry and Topology
Geometry and Topology Speaker: Viktoriya Ozornova (Ruhr-Universitaet Bochum) "Pasting diagrams in $(\infty,2)$-categories" Time: 11:30 Room: Zoom Meeting ID: 958 6908 4555 In the world of $(\infty,1)$-categories, it is well-known that the composition of specified morphisms is well-defined up to a contractible choice. The situation for $(\infty,2)$-categories is more subtle, as there are many potential ways of composing 2-cells. In a joint work in progress with Hackney, Riehl, Rovelli, we prove a uniqueness statement for the composition of so-called pasting diagrams, which I will explain during the talk. |
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5 Algebra Seminar
Algebra Seminar Speaker: Tung T. Nguyen (University of Chicago) "Power sums and special values of L-functions" Time: 14:30 Room: Zoom The zeta functions are a pillar of number theory. Zeta functions have been objects of great interest for number theorists due to their beauty, mystery, and power. I will discuss this study in the simplest case: the Hurwitz zeta functions. Recently, some surprising direct connections between the special values of Hurwitz zeta functions and power sums were found. In my talk, I will introduce these discoveries. In particular, we will see that special values of Hurwitz zeta functions have some nice integral representations. This is joint work with Jan Minac and Nguyen Duy Tan. |
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8 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Laurentiu Maxim (University of Wisconsin, Madison) "Hodge theory on Alexander invariants" Time: 15:30 Room: Zoom I will give an overview of recent developments in the study of Hodge-theoretic aspects of Alexander-type invariants associated with smooth complex algebraic varieties. Our results are motivated by (and can be regarded as global analogues of) similar statements for the Milnor fiber cohomology of complex hypersurface singularity germs. (Joint work with E. Elduque, C. Geske, M. Herradon-Cueto and B. Wang). |
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10 Geometry and Topology
Geometry and Topology Speaker: Ronnie Chen (University of Illinois Urbana-Champaign) "Gabriel-Ulmer duality for continuous categories" Time: 15:30 Room: Zoom Meeting ID: 958 6908 4555 The classical Gabriel-Ulmer duality asserts a dual adjoint equivalence between finitely complete categories, and a full sub-2-category of the complete, filtered-cocomplete categories which are known as locally finitely presentable (LFP). The definition of LFP category involves ``exactness conditions'' asserting compatibility between limits and
filtered colimits, together with a different sort of condition which amounts to admitting enough structure-preserving functors to Set; removing this last condition yields the continuous locally presentable (CLP) categories in the sense of Johnstone-Joyal. We prove an analog of Gabriel-Ulmer duality for all CLP categories, by replacing the dualizing
category Set with the category CPUMet of complete partial ultrametric spaces. As with Gabriel-Ulmer duality, this result has a logical interpretation, as a strong conceptual completeness theorem for the ``lex fragment'' of a continuous first-order logic for partial ultrametric structures. |
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12 Algebra Seminar
Algebra Seminar Speaker: Harris Daniels (Amherst College) "Entanglements of Division Fields of Elliptic Curves" Time: 14:30 Room: Zoom Central objects in the study of elliptic curves are the fields of definition of the points of order n. Relatively little is known about the way in which a fixed elliptic curve's division fields can intersect. In this talk, we lay the foundations for a systematic study of the entanglements of division fields of elliptic curves from a group theoretic perspective. In particular, we classify the way in which two prime-level division fields can intersect for infinitely many elliptic curves. This is joint work with Jackson S. Morrow. |
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17 Geometry and Topology
Geometry and Topology Speaker: Alexander Campbell (Macquarie University) "TBA" Time: 19:00 Room: Zoom Meeting ID: 958 6908 4555 |
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19 Algebra Seminar
Algebra Seminar Speaker: Nitin Chidambaram (MPI Bonn) "TBA" Time: 14:30 Room: Zoom |
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22 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Robin van der Veer (Leuven) "TBA" Time: 15:30 Room: Zoom |
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24 Geometry and Topology
Geometry and Topology Speaker: Ezra Getzler (Northwestern University) "TBA" Time: 19:00 Room: Zoom Meeting ID: 958 6908 4555 |
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26 Algebra Seminar
Algebra Seminar Speaker: Brandon Doherty (Western) "TBA" Time: 14:30 Room: Zoom |
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29 Geometry and Combinatorics
Geometry and Combinatorics Speaker: (Western) "no seminar this week" Time: 15:30 Room: |
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31 Geometry and Topology
Geometry and Topology Speaker: Ralph Kaufmann (Western) "Natural appearances of cubical structures" Time: 15:30 Room: Zoom Meeting ID: 958 6908 4555 Cubical structures appear naturally in several situations, sometimes clandestinely. In particular, we will consider such structures related to Feynman categories and discuss their origins. In this context, they appear for instance in coproduct structures, in a W-construction and relative W-constructions given via push-forwards, which give natural cubical complexes that are homotopy equivalent to moduli spaces. |
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Mathematics Calendar 
March 2021
