The TACO seminar focuses on topics in Topology, Algebra, Combinatorics, and Operators.
Webpages from previous semestersOrganizers: Emily Peters, Carmen Rovi
| March | ||
| 1 |
Chun-Ju Lai (Academia Sinica, Taiwan) | Quasi-hereditary covers, Hecke algebras, and quantum wreath product |
| 8 |
Spring break | |
| 15 |
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| 22 |
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| 29 |
Agustina Czenky (University of Oregon) |
Low rank symmetric fusion categories in positive characteristic. | April |
| 5 |
Cristina Sabando (Washington University) |
Joining the Odds and the idea for a monop |
| 12 |
Alessandro Arsie (University of Toledo) |
Reflection groups, integrable hierarchies and moduli spaces |
| 19 |
Maria Gillespie (Colorado State University)- on Zoom |
Equations defining M_{0,n}-bar as a projective variety |
| 26 |
Michael Klug (U Chicago) - in IES110 |
How not to study low-dimensional topology |
| Directions |
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IES (the institute for environmental sustainability) is located at the corner of W. Sheridan and N. Kenmore Avenues, Chicago, IL (map)
Some of the talks will be on zoom. If you would like to attend a zoom talk let one of the organizers know so we can add you to the list of participants.
| Abstracts |
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In this talk we introduce a new notion called the quantum wreath product that produces an algebra from a given algebra and a choice of parameters. Important examples include many variants of the Hecke algebras, such as (1) the cyclotomic Hecke algebras, (2) the affine Hecke algebras and their degenerate version, (3) Wan-Wang's wreath Hecke algebras, (4) Rosso-Savage's (affine) Frobenius Hecke algebras, and (5) the Hu algebra which quantizes the wreath product S_m wr S_2 between symmetric groups. Our uniform approach to both its structure and representation theory encompasses many known results which were proved in a case by case manner. I'll also talk about an application regarding the Ginzburg-Guay-Opdam-Rouquier problem on quasi-hereditary covers of Hecke algebras. This is a joint work with Dan Nakano and Ziqing Xiang
In this talk, we look at the classification problem for symmetric fusion categories in positive characteristic. We recall the second Adams operation on the Grothendieck ring and use its properties to obtain some classification results. In particular, we show that the Adams operation it is not the identity for any non-trivial symmetric fusion category. We also give lower bounds for the rank of a (non-super-Tannakian) symmetric fusion category in terms of p. As an application of these results, we classify all symmetric fusion categories of rank 3 and those of rank 4 with exactly two self-dual simple objects.
Monops were introduced by Mendez and Sanchez to give a combinatorial explanation of the inverse of Riordan Matrices by means of Moebius inversion over partially ordered sets. In this talk we study two posets with a common monop structure and give a combinatorial interpretation of their Moebius inversion.
Since Kontsevich's proof of Witten's conjecture in the 90s, integrable hierarchies of PDEs have appeared as an important tool (and a surprising connection!) in the exploration of the topology of moduli spaces of stable curves. In this talk, I will review the prototypical result in this area, and I will present a panoramic view of some work I have done with a variety of collaborators in the past several years connecting (dispersionless) integrable hierarchies, orbits spaces of real and complex reflection groups, Frobenius, flat and bi-flat F-manifolds on one side and F-Cohomological Field Theories, dispersive integrable hierarchies and moduli spaces of stable curves on the other.
Abstract: Monin and Rana conjectured a set of equations defining the image of the moduli space M_{0,n}-bar under an embedding into P^1 x P^2 x ... x P^{n-3} due to Keel and Tevelev, and verified the conjecture for n less than or equal to 8 using Macaulay2. We have proven this conjecture for all n, and in this talk I will give an outline of our proof methods. This is joint work with Sean Griffin and Jake Levinson.
Abstract: Stallings gave a group-theoretic approach to the 3-dimensional Poincare conjecture that was later turned into a group-theoretic statement equivalent to the Poincare conjecture by Jaco and Hempel and then proven by Perelman. Together with Blackwell, Kirby, Longo, and Ruppik, we have extended Stallings's approach to give group-theoretically defined sets that are in bijection with (i) closed 3-manifolds, (ii) closed 3-manifolds with a link, (iii) closed 4-manifolds, and (iv) closed 4-manifolds with a link (of surfaces). I will explain these bijections and how this results in an algebraic formulation of the unknotting conjecture and a group-theoretic characterization of 4-dimensional knot groups.
