Heisenberg homology of surface configurations We study the action of the mapping class group of Σ=Σ_{g,1} on
the homology of configuration spaces with coefficients twisted by the discrete Heisenberg group H=H(Σ).
We will specialise to the Schrödinger representation and its finite
dimensional analogue in which case we obtain representations of a
central extension of the mapping class group.

Sabin Cautis* (University of British Columbia)

TBA TBA

Nicolle Gonzalez (UCLA)

TBA TBA

Eugene Gorsky* (UC Davis)

Tautological classes and symmetry in Khovanov–Rozansky homology We define a new family of commuting operators F_{k}
in Khovanov–Rozansky link homology, similar to the
action of tautological classes in cohomology of
character varieties. We prove that F_{2} satisfies
``hard Lefshetz property" and hence exhibits the
symmetry in Khovanov–Rozansky homology conjectured by
Dunfield, Gukov and Rasmussen. This is a joint work
with Matt Hogancamp and Anton Mellit.

Sergei Gukov (Caltech)

TBA TBA

Mikhail Khovanov* (Columbia University)

Topological theories and automata TBA Joint work with Mee Seong Im.

Lukas Lewark (Universität Regensburg)

Khovanov homology and rational unknotting TBA

Robert Lipshitz* (University of Oregon)

Khovanov homology and non-orientable surfaces The first half of the talk will introduce an
invariant of non-orientable knot cobordisms, coming
from deformed Khovanov homology, imitating the
construction of the Heegaard Floer mixed invariant
(i.e., the Seiberg–Witten invariant). The second half
will discuss properties and computations of Khovanov
homology invariants of cobordisms, including
leveraging work of Hayden–Sundberg to show that they
distinguish some exotic pairs of non-orientable
surfaces. This is joint with Sucharit
Sarkar.

Andrew Lobb (Durham University)

TBA TBA

Ciprian Manolescu* (Stanford)

A knot Floer stable homotopy type Given a grid diagram for a knot or link K in 𝕊^{3},
we construct a spectrum whose homology is the knot
Floer homology of K. We conjecture that the homotopy
type of the spectrum is an invariant of K. Our
construction does not use holomorphic geometry, but
rather builds on the combinatorial definition of grid
homology. We inductively define models for the moduli
spaces of pseudo-holomorphic strips and disk bubbles,
and patch them together into a framed flow
category. The inductive step relies on the vanishing
of an obstruction class that takes values in a complex
of positive domains with partitions. (This is joint
work with Sucharit Sarkar.)

Anton Mellit (Universität Wien)

TBA TBA

Ina Petkova* (Darthmouth College)

Annular
link Floer homology and 𝖌𝖑(1|1) The Reshetikhin–Turaev
construction for the quantum
group U_{q}(𝖌𝖑(1|1)) sends tangles to
ℂ(q)-linear maps in such a way that a
knot is sent to its Alexander polynomial. Tangle Floer
homology is a combinatorial generalization of knot
Floer homology which sends tangles to (homotopy
equivalence classes of) bigraded dg bimodules. In
earlier work with Ellis and Vertesi, we show that
tangle Floer homology categorifies a
Reshetikhin–Turaev invariant arising naturally
in the representation theory
of U_{q}(𝖌𝖑(1|1)); we further construct
bimodules E and F corresponding
to E, F in U_{q}(𝖌𝖑(1|1)) that
satisfy appropriate categorified relations. After a
brief summary of this earlier work, I will discuss how
the horizontal trace of the E and F
actions on tangle Floer homology gives a 𝖌𝖑(1|1)
action on annular link Floer homology that has an
interpretation as a count of certain holomorphic
curves. This is based on joint work in progress with
Andy Manion and Mike Wong.

Jacob Rasmussen* (University of Cambridge)

Knot Floer homology, sutures, and the solid torus TBA

Marko Stosic* (Universidade de Lisboa)

Knot invariants, knot complements and quivers In this talk I will give an overview of the knots-quivers correspondence, from the first formulation till some of the recent results.
Originally knots-quivers correspondence was introduced by rewriting colored HOMFLY-PT invariants in the form of quiver generating series for suitable quivers.
Recently, other knot invariants have also been shown to be re-writable in a "quiver form", namely Gukov–Manolescu Ẑ-invariants of knot complements.
I will present some basic facts about these correspondences, as well as relations between them.

Joshua Sussan (CUNY)

p-DG structures in higher representation theory One of the goals of the categorification program
is to construct a homological invariant of 3-manifolds
coming from the higher representation theory of
quantum groups. The WRT 3-manifold invariant uses
quantum groups at a root of unity. p-DG theory was
introduced by Khovanov as a means to categorify
objects at prime roots of unity. We will review this
machinery and show how to construct categorifications
of certain representations of quantum 𝖘𝖑(2) at prime
roots of unity.

Pedro Vaz (Université Catholique de Louvain)

2-Verma
modules and link homologies In this talk
I will explain how 2-Verma modules can be used to
produce several link homologies for knots in the
3-space and in the solid torus. The various
constructions go through a categorification of
(parabolic) Verma modules and its tensor products with
finite-dimensional irreducibles of 𝖌𝖑(n). The
material presented spreads along several
collaborations with Abel Lacabanne, and Grégoire
Naisse.

Emmanuel Wagner (Université de Paris)

Categorification of
colored Jones polynomial at root of unity
In the first part of the talk, we will define colored
symmetric 𝖌𝖑(2) homologies. These are
homological link invariants. We'll focus on a
combinatorial and elementary approach of this
construction and explain how it is related to Soergel
bimodules and to triply graded homology. In the second
part, we'll see how to endow them with pDG structures
and providing so a categorification of colored Jones
polynomial at root of unity. This is a joint work with
You Qi, Louis-Hadrien Robert and Joshua Sussan.

Paul Wedrich (Universität Hamburg)

A skein relation for singular Soergel bimodules Soergel bimodules categorify Hecke algebras and
lead to invariants of braids that take values in
monoidal triangulated categories. In this process, the
quadratic `skein relation' on Artin generators is
promoted to a distinguished triangle. I will talk
about an analog of this relation in the setting of
singular Soergel bimodules and Rickard complexes, in
which the distinguished triangle gets replaced by a
longer one-sided twisted complex. Joint work with
M. Hogancamp and D.E.V. Rose.