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March 2021

Tsao-Hsien Chen, University of Minnesota – Geometric Methods in Representation Theory Seminar

March 19 @ 4:00 pm - 5:00 pm

Tsao-Hsien Chen, University of Minnesota Time: 4:00 pm, 03/19/21 Title: Towards derived Satake equivalence for symmetric varieties Abstract: In an ongoing project of  D. Ben-Zvi, Y. Sakellaridis and A. Venkatesh, the authors propose a conjectural generalization of the derived Satake equivalence for complex reductive groups to spherical varieties. I will describe a program aimed at establishing their conjecture in the case of symmetric varieties (an important class of spherical varieties). A key ingredient is the relation between the Satake category for…

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Alex Weekes, University of British Columbia – Geometric Methods in Representation Theory Seminar

March 26 @ 4:00 pm - 5:00 pm

Alex Weekes, University of British Columbia Title:  Coulomb branches symmetrizable types Abstract: Braverman-Finkelberg-Nakajima have recently given a mathematical construction of the Coulomb branches for 3d N=4 theories. From a representation-theoretic perspective, one reason that their work is especially appealing is that affine Grassmannian slices of ADE types arise this way, associated to quiver gauge theories. By allowing general quivers, Coulomb branches also provide a candidate definition for affine Grassmannian slices in all symmetric Kac-Moody types. In this talk I will discuss joint work with Nakajima, where…

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September 2021

Calvin McPhail-Snyder, Duke – Geometric Methods in Representation Theory Seminar

September 23 @ 4:00 pm - 5:00 pm

Title: Quantum invariants from unrestricted quantum groups Abstract: Quantum groups are a central part of the construction of quantum invariants of knots, links, and 3-manifolds. Existing work focuses mainly on the case where the quantization parameter q is generic, or on the semisimplified theory at q a root of unity. In this talk, I will discuss how to construct invariants of knots (and links) using the non-semisimple part of unrestricted quantum sl_2 at a root of unity. These “holonomy invariants”…

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October 2021

Calvin McPhail-Snyder, Duke – Geometric Methods in Representation Theory Seminar

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

Title: Quantum invariants from unrestricted quantum groups Abstract: Quantum groups are a central part of the construction of quantum invariants of knots, links, and 3-manifolds. Existing work focuses mainly on the case where the quantization parameter q is generic, or on the semisimplified theory at q a root of unity. In this talk, I will discuss how to construct invariants of knots (and links) using the non-semisimple part of unrestricted quantum sl_2 at a root of unity. These “holonomy invariants” turn out…

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Olivia Dumitrescu, UNC-Chapel Hill – Geometric Methods in Representation Theory Seminar

October 8 @ 4:00 pm - 5:00 pm

In-Person Phillips Hall, Room 385

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Iva Halacheva, Northeastern – Geometric Methods in Representation Theory Seminar

October 15 @ 4:00 pm - 5:00 pm

Iva Halacheva, Northeastern Zoom: 930 8567 8674 Passcode: email unc_math@unc.edu for passcode Title: Categorical and geometric realizations of cactus group actions on crystals Abstract: One approach to studying the representation theory of Lie algebras and their associated quantum groups is through combinatorial shadows known as crystals. While the original representations carry an action of the braid group, their crystals carry an action of a closely related group known as the cactus group. I will describe how we can realize this…

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Chiara Damiolini, University of Pennsylvania – Geometric Methods in Representation Theory Seminar

October 29 @ 4:00 pm - 5:00 pm

Over Zoom

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November 2021

David Nadler, UC Berekley – Geometric Methods in Representation Theory Seminar

November 5 @ 2:30 pm - 3:30 pm

Location: Phillips Hall, Room 385 Time: 2:30 – 3:30 pm Speaker: David Nadler, UC Berkeley Title: Betti Geometric Langlands Abstract: I'll introduce Betti Geometric Langlands through some key objects, conjectures and results. Then I'll discuss recent and ongoing work with Zhiwei Yun devoted to constructing some of its expected topological field theory structures.

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Xuqiang Qin, UNC-Chapel Hill – Geometric Methods in Representation Theory Seminar

November 12 @ 4:00 pm - 5:00 pm

Mode: In-Person Location: Phillips Hall 385 Title: Minimal instantons on Fano threefolds and compactifications of their moduli spaces Abstract: Instanton bundles were first introduced on P^3 as stable rank 2 bundles E with c1(E)=0 and H^1(E(-2))=0. Torsion free generalizations and properties of moduli spaces of instanton bundles have been widely studied. Faenzi and Kuznetsov generalized the notion of instanton bundles to other Fano threefolds. In this talk, we look at semistable sheaves of rank 2 with Chern classes c1 =…

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Hang Huang, Texas A&M – Geometric Methods in Representation Theory Seminar

November 19 @ 4:00 pm - 5:00 pm

Over Zoom

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