Contact:

Catharina Stroppel email

Daniel Tubbenhauer email

- Seminar room 1.008, Mathematik-Zentrum, Endenicher Allee 60, 53115 Bonn, Germany
- Every (second) Friday from 14:15-15:15 (with some exceptions)
- There will be a lecture series of Dennis Gaitsgory:
- The first lecture will take place Tuesday 10.01.2016 from 16:30-18:30 in the lecture hall of the MPIM
- The second lecture will take place Wednesday 11.01.2016 from 14:00-16:00 in the Lipschitz-Saal, Mathematik-Zentrum, Endenicher Allee 60
- The third lecture will take place Friday 13.01.2016 from 12:30-14:30 in the lecture hall of the MPIM
- There is an extra website available: Lecture series home

- David Jordan's talk will not take place October the 28th and is canceled
- Emily Norton's talk is scheduled for Tuesday the 20.12.2016, 14:15-15:15, Seminarraum, Max-Planck-Institut für Mathematik (MPIM)
- Olivier Schiffmann's talk will not take place January the 20th and is canceled
- Kevin Coulembier's is scheduled for Monday the 20.02.2017, 13:15-14:15, Hörsaal, Max-Planck-Institut für Mathematik (MPIM)
- First talk: Friday 21.10.2016

- Friday 21.10.2016,
**Speaker**: Inna Entova Eisenbud (Hebrew University of Jerusalem),**Title**: On finite-dimensional representations of the Lie superalgebra $P(n)$ - Friday 28.10.2016,
**Speaker**: Talk canceled! David Jordan (University of Edinburgh),**Title**: The quantum Springer sheaf - Friday 11.11.2016,
**Speaker**: Andrew Hubery (Universität Bielefeld),**Title**: Euler characteristics of quiver Grassmannians - Friday 18.11.2016,
**Speaker**: Jonathan Comes (The College of Idaho),**Title**: Jellyfish partition categories - Friday 25.11.2016,
**Speaker**: Andrew Mathas (University of Sydney),**Title**: Alternating Hecke algebras - Friday 02.12.2016,
**Speaker**: Zhengfang Wang (Université Paris Diderot-Paris 7),**Title**: Singular Hochschild cohomology and higher algebraic structures - Friday 16.12.2016,
**Speaker**: Chun-Ju Lai (University of Virginia),**Title**: Affine Hecke algebras and quantum symmetric pairs - Tuesday 20.12.2016,
**Speaker**: Emily Norton (MPIM Bonn),**Title**: Decomposition numbers for rational Cherednik algebras - Tuesday 10.01.2016,
**Speaker**: Dennis Gaitsgory (Harvard University),**Title**: Hirzebruch-Riemann-Roch as a categorical trace I - Wednesday 11.01.2016,
**Speaker**: Dennis Gaitsgory (Harvard University),**Title**: Hirzebruch-Riemann-Roch as a categorical trace II - Friday 13.01.2016,
**Speaker**: Dennis Gaitsgory (Harvard University),**Title**: Hirzebruch-Riemann-Roch as a categorical trace III - Friday 20.01.2017,
**Speaker**: Talk canceled! Olivier Schiffmann (Université de Paris-Sud Orsay),**Title**: Cohomological Hall algebras of quivers - Friday 03.02.2017,
**Speaker**: Vanessa Miemietz (University of East Anglia),**Title**: Simple transitive 2-representations via coalgebra $1$-morphisms - Monday 20.02.2017,
**Speaker**: Kevin Coulembier (University of Sydney),**Title**: The periplectic Brauer algebra - Friday 24.02.2017,
**Speaker**: Jieru Zhu (University of Oklahoma),**Title**: Presenting cyclotomic Schur algebras

Inna Entova Eisenbud,

**Title**: On finite-dimensional representations of the Lie superalgebra $P(n)$

In this talk, I will present some of the results we obtained concerning the category $\mathrm{Rep}(P(n))$ of finite-dimensional representations. Unlike the rest of the classical-type Lie superalgebras, the structure of this category has not been well understood until now.

I will explain the classification of blocks in this category, the combinatorics behind the Kazhdan-Lusztig coefficients, and present a categorical action of the infinite Temperley-Lieb algebra through translation functors.

This is part of a joint project with M. Balagovic, Z. Daugherty, M. Gorelik, I. Halacheva, J. Hennig , M. Seong Im, G. Letzter, E. Norton, V. Serganova, C. Stroppel.

The talk will not assume prior knowledge of Lie superalgebras.

Talk canceled! David Jordan,

**Title**: The quantum Springer sheaf

Most traditionally, the Springer sheaf is constructed geometrically, in the language of Borel-Moore homology and perverse sheaves; however Hotta and Kashiwara gave it a purely algebraic reincarnation in the language of equivariant $D(\mathfrak{g})$-modules.

In this talk, I'll explain some joint work with Monica Vazirani, to define and compute the so-called quantum Springer sheaf, which plays an analogous role for the quantum group $\boldsymbol{\mathrm{U}}_q(\mathfrak{g})$. Our main tool to study these is a “genus one” Schur-Weyl duality type functor to representations of the double affine Hecke algebra.

Andrew Hubery,

**Title**: Euler characteristics of quiver Grassmannians

Jonathan Comes,

**Title**: Jellyfish partition categories

Andrew Mathas,

**Title**: Alternating Hecke algebras

Zhengfang Wang,

**Title**: Singular Hochschild cohomology and higher algebraic structures

In this talk, we construct a singular version of Hochschild cochain complex to compute the singular Hochschild cohomology. We prove that there is a Gerstenhaber algebra structure in the singular Hochschild cohomology and this structure has a prop interpretation. We discuss the singular version of Deligne conjecture, which is related to the higher algebraic structures (for instance, the $B_{\infty}$-algebra and homotopy Gerstenhaber algebra structures). The Batalin-Vilkovisky (BV) algebra structure is also constructed in the case of symmetric Frobenius algebras. If time allows, we will talk about some results of a joint-work in progress with Manuel Rivera in the application of singular Hochschild cohomology to string topology.

Chun-Ju Lai,

**Title**: Affine Hecke algebras and quantum symmetric pairs

In this talk I will focus on the Hecke algebraic approach and present our work on a generalization to affine type $C$, which produces favorable bases for q-Schur algebras and certain coideal subalgebras of quantum groups of affine type $A$. We further show that these algebras are examples of quantum symmetric pairs, which are quantization of symmetric pairs consisting of a Lie algebra and its fixed-point subalgebra associated to an involution.

This is a joint work with Z. Fan, Y. Li, L. Luo, and W. Wang.

Emily Norton,

**Title**: Decomposition numbers for rational Cherednik algebras

Dennis Gaitsgory,

**Title**: Hirzebruch-Riemann-Roch as a categorical trace

However, in order to carry out our program, we will need to venture into the world of higher categories: the 2-category we will be working with consists of DG-categories, the latter being higher categorical objects. And the process of calculation of the categorical trace will involve derived algebraic geometry: the key geometric player will be the self-intersection of the diagonal of $X$, a.k.a. the inertia (derived) scheme of $X$.

So, this series of talks can be regarded as providing a motivation for studying higher category theory and derived algebraic geometry: we will use them in order to prove an equality of numbers. That said, we will try to make these talks self-contained, and so some necessary background will be supplied.

Talk canceled! Olivier Schiffmann,

**Title**: Cohomological Hall algebras of quivers

Vanessa Miemietz,

**Title**: Simple transitive 2-representations via coalgebra $1$-morphisms

Kevin Coulembier,

**Title**: The periplectic Brauer algebra

Jieru Zhu,

**Title**: Presenting cyclotomic Schur algebras