The ICART seminar usually meets on Tuesdays and/or Thursdays in Math 528, after tea (around 4:15pm) unless noted otherwise (in red).
Previous semesters:
| Date | Speaker | Title |
| Sept. 8 | Alexander Ellis Columbia |
Odd symmetric functions and the odd nilHecke algebra |
| Sept. 22 | Noah Snyder Columbia |
3D TQFTs and finite tensor categories |
| Oct. 6 | Sachin Gautam Columbia |
Yangians and quantum loop algebras |
| Oct. 18 | Pedro Vaz University of Zurich and IST Lisbon |
Categorified q-Schur algebra and the BMW algebra |
| Oct. 20 | Ben Cooper University of Virginia |
Handle slides and localizations |
| Oct. 25 | Anton Zeitlin Yale |
Quantum group as semi-infinite cohomology |
| Oct. 27 | Anton Zeitlin Yale |
Loop ax+b group, gamma-function and modular double |
| Nov. 15 | Michael McBreen Princeton |
Introduction to geometric representation theory |
| Nov. 29 | Yanhong Yang Columbia |
Introduction to crystalline cohomology, part 1 |
| Dec. 1 | Yanhong Yang Columbia |
Introduction to crystalline cohomology, part 2 |
| TBA | Sachin Gautam Columbia |
Yangians and quantum loop algebras, part 2 |
Abstracts
September 8, 2011. Alexander Ellis, "Odd symmetric functions and the odd nilHecke algebra"
The odd symmetric functions form a Z-graded Hopf superalgebra which exhibits signed analogues of many of the combinatorial properties of the classical symmetric functions, despite being non-commutative and non-cocommutative. I will review the classical and the odd combinatorics, as well as perhaps the connection with the quantum quasi-symmetric functions of Thibon and Ung. I will also explain how the odd symmetric functions arise in the odd categorification of quantum groups and, conjecturally, odd Khovanov homology. Joint with Mikhail Khovanov and Aaron Lauda.
September 22, 2011. Noah Snyder, "3D TQFTs and finite tensor categories"
October 6, 2011. Sachin Gautam, "Yangians and quantum loop algebras"
In this introductory talk I will go over the definitions and basic properties of Yangians and quantum loop algebras, with a special emphasis on the similarities between the two algebras. I will also present a degeneration argument (due to Drinfeld) which allows one to reconstruct the former from the later.
October 18, 2011. Pedro Vaz, "Categorified q-Schur algebra and the BMW algebra"
In 1989 François Jaeger showed that the the Kauffman polynomial ofa link L can be obtained as a weighted sum of HOMFLYPT polynomials on certain links associated to L. In this talk I will explain how to use a version of Jaeger's theorem to stablish a connection between the SO(2N)-BMW and the q-Schur algebras. I will then present a subcategory of the Schur category which categorifies the SO(2N)-BMW algebra (joint with E. Wagner).
October 20, 2011. Ben Cooper, "Handle slides and localization"
I will discuss an approach to evaluating some categorifications at a root of unity based on the categorified Jones-Wenzl projectors. Within this construction I will define some objects which are invariant under handle slides.
October 25, 2011. Anton Zeitlin, "Quantum group as semi-infinite cohomology"
It will be shown how to obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. The construction of $GL_q(2)$ as semi-infinite cohomology and the vertex-algebraic construction of the noncommutative Laplace operator on $GL_q(2)$ will be outlined.
October 27, 2011. Anton Zeitlin, "Loop ax+b group, gamma-function and modular double"
The first half of the talk will be devoted to the modular double of a quantum group and related representation theory of the quantum plane and ax+b group. After that I will explain the construction of the representations of the central extension of the loop ax+b group on the Hilbert space of square integrable functions with respect to Wiener measure.
November 29 and December 1, 2011.Yanhong Yang, "Introduction to crystalline cohomology"
In the first talk, I will give a brief introduction to crystalline
cohomology; and in the second one, I will talk about the equivalence
between the category of a unit-root F-isocrystals of rank r and the
category of representations \pi_1(X)-->GL(r, W(F_q)) and a purity
theorem of the stratification by Newton polygons from F-isocrystal.
References:
1) Note on crystalline cohomology, by Ogus and Berthelot;
2) An improvement of de Jong-Oort's purity Theorem, by Y.
Yang arXiv:1004.3090
3)(For the equivalence of categories, see Prop 4.1.1) p-adic
properties of modular schemes and modular forms, Modular Functions of
One Variable. III, Lecture Notes in Math., vol. 350, 113-164 by Katz