Geometry and Topology

Speaker: Ben Williams (UBC)

"The EHP sequence in A1 algebraic topology"

Time: 15:30

Room: MC 107

The classical EHP sequence is a partial answer to the question of how far the unit map of the loop-suspension adjunction fails to be a weak equivalence. It can be used to move information from stable to unstable homotopy theory. I will explain why there is an EHP sequence in A1 algebraic topology, and some implications this has for the unstable A1 homotopy groups of spheres.

Noncommutative Geometry

Speaker: (Western)

"Higgs fields and symmetry breaking mechanism "

Time: 11:30

Room: MC 107

Existence of massive gauge bosons breaks down the local gauge invariance of Yang-Maills Lagrangians. In this lecture we shall look at one method to deal with this situation through the introduction of Higgs fields.

Homotopy Theory

Speaker: Marco Vergura (Western)

"Equivalences and the Univalence Axiom (part 2)"

Time: 13:30

Room: MC 107

Following Chapter 4 of the HoTT book, we continue our journey in the various characterizations of equivalences in Type Theory. We also show how Function Extensionality follows from the Univalence Axiom.

Analysis Seminar

Speaker: Josue Rosario-Ortega (Western)

"Special Lagrangian submanifolds with edge-singularities"

Time: 15:30

Room: MC 107

Given a Calabi-Yau manifold $(M,\omega,\Omega)$ of complex dimension $n$, a Special Lagrangian submanifold (SL-submanifold) $L\subset M$ is a real $n$ dimensional submanifold calibrated by $\text{Re}\:\Omega$. These type of submanifolds are Lagrangian with respect to the symplectic structure $\omega$ and minimal with respect to the Calabi-Yau metric of the ambient space. Singular SL-submanifolds are particularly important as they play a fundamental role in mirror symmetry. In this talk I will survey the results obtained in the last years on deformation and moduli spaces of SL-submanifolds with conical singularities. Moreover I will introduce SL-submanifolds with higher order singularities (in particular edge singularities) and I will explain the approach used by the speaker to study moduli spaces of such type of singularities and some results obtained about the moduli space.

Geometry and Combinatorics

Speaker: Sergio Chaves (Western)

"The Borel construction (Part 2)"

Time: 16:00

Room: TC 342

Let $X$ be a topological space with an action of a topological group $G$. We want to relate to $X$ an algebraic object that reflects both the topology and the action of the group. The first candidate is the cohomology ring $H^{*}(X/G)$: however, if the action is not free, the space $X/G$ may have some pathology. The Borel construction allows to replace $X$ by a topological space $X'$ which is homotopically equivalent to $X'$ and the action of $G$ on $X'$ is free.

Noncommutative Geometry

Speaker: Rui Dong (Western)

"Classification of Finite Real Spectral Triples"

Time: 11:30

Room: MC 107

First, I give a basic introduction to finite noncommutative spaces, and then I focus on the classification of finite real spectral triples.

Basic Notions Seminar

Speaker: Lex Renner (Western)

"Hilbert's Fourteenth Problem"

Time: 15:30

Room: MC 107

Hilbert's Fourteenth Problem asks about the finite generation of certain commutative rings. Furthermore, Hilbert's question was a major catalyst in the development of geometric invariant theory. But the basic question here makes sense more generally. I will discuss examples, successes, myths, and new approaches.

Algebra Seminar

Speaker: Christin Bibby (Western)

"Representation stability for the cohomology of arrangements"

Time: 16:00

Room: MC 107

From a root system, one may consider the arrangement of reflecting hyperplanes, as well as its toric and elliptic analogues. The corresponding Weyl group acts on the complement of the arrangement and hence on its cohomology. We consider a sequence of linear, toric, or elliptic arrangements which arise from a family of root systems of type A, B, C, or D, and we study the stability of the rational cohomology as a sequence of Weyl group representations. Our techniques combine a Leray spectral sequence argument similar to that of Church in the type A case along with $FI_W$-module theory which Wilson developed and used in the linear case.