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Weekly research seminar
List of talks
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May 21, 2025, 10:15 a.m.
Lorenzo Sadun (University of Texas at Austin)
Tiling spaces, inverse limits and cohomology
Tiling dynamical systems are of both topological and dynamical interest. The set of tilings with a given local structure is a ``matchbox manifold'', locally modeled on the product of a Cantor set with Euclidean space. …
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May 14, 2025, 10:15 a.m.
Dominik Gdesz (UWr)
Khovanov-Rozansky homology of torus links
In 2019 Matthew Hogancamp and Anton Mellit used the Soergel bimodules approach to Khovanov-Rozansky homology to compute it in the case of torus links T(m,n) for non-negatuve m,n. We show an outline of this computation …
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April 30, 2025, 10:15 a.m.
Joachim Jelisiejew (MIM UW)
Algebraic links and affine Springer fibers
I will explain affine Springer theory and its connections to Hilbert schemes, braid varieties. This is the last big object in the Gorsky-Kivinen-Simental notes. I will also cover connections to the previous lectures in the …
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April 23, 2025, 10:15 a.m.
Piotr Kucharski
Knot-quiver correspondence and the topological invariants
In this talk I will introduce the knot-quiver correspondence with a special emphasis of the role of the Labastida-Marino-Ooguri-Vafa invariants of knots and Donaldson-Thomas invariants of quivers.
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April 16, 2025, 10:15 a.m.
Yuze Luan (IMPAN)
Hilbert scheme of points on singular curves and the Khovanov-Rozansky homology
We will define and compute some concrete examples of the homologies of the punctual Hilbert schemes of points on singular plane curves. We will also compute some examples of the Khovanov- Rozansky homologies of some …
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April 9, 2025, 10:15 a.m.
Maciej Borodzik (MIM UW)
Khovanov-Rozansky theories in terms of matrix factorisations
We give a sketch of a construction of Khovanov-Rozansky homology via matrix factorization. We focus on explaining the rich homological structure of the construction. The work is based on Khovanov-Rozansky original construction and on the …
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March 26, 2025, 10:15 a.m.
Wojciech Politarczyk (MIM UW)
Soergel bimodules and Khovanov-Rozansky HOMFLY-PT homology
Abstract: We will outline the constructions of the Khovanov-Rozansky HOMFLY-PT homology, which categorifies the HOMFLY-PT polynomial. Additionally, we will discuss basic properties of this invariant.
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March 19, 2025, 10:15 a.m.
Mieszko Baszczak (MIM UW)
Braid Varieties
I will talk about braid varieties which are certain objects defined via braids. They have a lot of connections, for example with links, point counting and flag varieties. In my talk I will focus on …
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March 12, 2025, 10:15 a.m.
Robert Szafarczyk (University of Copenhagen)
An obstruction to lifting schemes to spectral schemes
There is a relatively simple purly algebraic obstruction, due to Nikolaus, for lifting commutative rings to the sphere spectrum. As an application, it recovers a classical result on non-existence of fully commutative multiplicative structures on …
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March 5, 2025, 10:15 a.m.
Mikołaj Rotkiewicz (MIMUW)
On classical algebraic structures on higher-order analogs of Lie Algebroids (O klasycznych strukturach algebraicznych na wyższych analogach algebroidów Liego)
Pojęcie \emph{algebroidu wyższego rzędu}, wprowadzone w pracy \emph{Higher-order analogs of Lie algebroids via vector bundle comorphisms} (M. Jóźwikowski, M. Rotkiewicz, SIGMA 2018), stanowi uogólnienie zarówno wiązki stycznej rzędu $k$, $\tau^k_M: \mathrm{T}^k M \to M$, jak …
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Jan. 15, 2025, 10:30 a.m.
Marcin Chałupnik (MIMUW)
Moduły Yettera-Drinfelda nad algebrą Steenroda i kategorie funktorów
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Oct. 16, 2024, 10:30 a.m.
Arturo Espinosa Baro (UAM)
(Sequential) topological complexity of aspherical spaces and sectional categories of subgroup inclusions
The topological complexity (TC) of a topological space is a homotopy invariant introduced by M. Farber to study the order of instability of motion planning algorithms of configuration spaces of mechanical and autonomous systems. Different …
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Oct. 9, 2024, 10:30 a.m.
Andrzej Weber (MIMUW)
Basics about elliptic characteristic classes and singularities (Podstawy o eliptycznych klasach charakterystycznych i osobliwościach)
I will motivate why the elliptic characteristic classes are well adapted to study singular algebraic varieties. The blow-up relation forces that the formal power series defining elliptic classes is up to a modificarion equal to …
