Geometry and Combinatorics

Speaker: Antony Della Vecchia (TU Berlin)

"Partial Algebraic Shifting"

Time: 15:30

Room: MC 108

We give an overview of algebraic shifting in the exterior algebra and consider partial algebraic shifting as a generalisation thereof. We then look at families of partial algebraic shifts parameterized by the symmetric group and provide a sufficient condition for preserving the Betti numbers and shifting to a near cone.

Geometry and Topology

Speaker: Anibal Medina-Mardones (Western)

"Bidifferential Complexes and the Hodge Decomposition"

Time: 15:30

Room: MC 107

This talk is primarily expository and aimed at graduate students and newcomers to homotopical algebra. We will introduce the language of bidifferential complexes--graded vector spaces equipped with both a differential and a codifferential--and use it to discuss deformation retractions and an algebraic form of the Hodge decomposition.

We will then examine in more detail the classical setting of differential forms on a Riemannian manifold, focusing on the homotopy transfer of the wedge product, which yields a complete invariant of its rational homotopy type.

In a subsequent talk, I plan to move beyond the Riemannian case and consider the Lorentzian setting, where physical information is also encoded in the transferred structure.

Transformation Groups Seminar

Speaker: Tao Gong (Western)

"Homotopy types of compact 1-connected 4-dimensional CW complexes"

Time: 09:30

Room: MC 108

A compact 1-connected 4-dimensional CW complex has its homotopy type determined by its cohomology ring together with the Bockstein homomorphisms and the Pontryagin squares. This result has many applications, including to the cohomology rigidity problem. Following the work of J. H. C. Whitehead, we will see that morphisms between such cohomology rings can be lifted to maps between CW complexes.

Algebra Seminar

Speaker: Saleh Ahmed (Western)

"An introduction to rigid geometry."

Time: 14:30

Room: MC 107.

Algebra Seminar

Speaker: Saleh Ahmed (Western)

"An introduction to rigid geometry."

Time: 14:30

Room: MC 107

Geometry and Topology

Speaker: Anibal Medina-Mardones (Western)

"Homotopy Lie algebras and Gauge Theories"

Time: 15:30

Room: MC 107

In this talk we survey an algebro-homotopical perspective on classical gauge field theories in the perturbative regime. We show how cyclic $L_\infty$-algebras encode their essential structures, among them fields, symmetries, and actions. We illustrate this perspective through three central examples: Maxwell's electromagnetism, Chern-Simons theory, and Yang-Mills theory.

Transformation Groups Seminar

Speaker: Vladimir Gorchakov (Western)

"Equivariant formality and the cohomology of subgroups of Right-Angled Coxeter Groups"

Time: 09:30

Room: MC 107

Let $H$ be a subgroup of $(\mathbb{Z}_2)^m$ acting on a real moment-angle complex. In this talk, I will discuss when the H-action is equivariantly formal and how this follows from similar results on torus actions on moment-angle complexes. As an application, I will discuss the cohomology of subgroups of Right-Angled Coxeter Groups. This talk is based on ongoing joint work with S. Amelotte.

Algebra Seminar

Speaker: Hyun Kim (Western)

"Aspects of etale sheaves"

Time: 14:30

Room: MC 107

I will briefly discuss some of the essential concepts that one speaks of in the theory of sheaves on the small etale sites of schemes, such as the etale fundamental group, locally constant sheaves, ell-adic sheaves, etale cohomology, and ell-adic cohomology. Time permitting, I will also state theorems about ell-adic cohomology such as the Grothendieck-Lefschetz Trace Formula, Poincare duality, and the Weil conjectures.