Geometry and Topology

Speaker: Boris Chorny (Haifa)

"Homotopy theory of homotopy presheaves"

Time: 15:30

Room: MC 107

We will discuss the category small functors from a combinatorial model category to simplicial sets and introduce a model structure in which the fibrant objects are the levelwise fibrant homotopy functors. This model structure is called the homotopy model structure.

Next, we will discuss the conditions under which a Quillen equivalence of model categories induces a Quillen equivalence of the homotopy model structures. If the time permits, then we will describe an alternative model structure Quillen equivalent to the homotopy model structure.

This work is joint with D. White.

Analysis Seminar

Speaker: Almut Burchard (Toronto)

"Symmetrization and sharp functional inequalities"

Time: 15:30

Room: MC 108

Symmetric decreasing rearrangement replaces a given function $f$ on $\mathbb{R}^d$ by a radially decreasing function $f^*$ that is equimeasurable to $f$. Symmetrization techniques have been used to determine the sharp constants in classical functional inequalities such as the Sobolev inequality, and for solving minimization problems in Geometry and Mathematical Physics. Symmetrization also motivates the definition of rearrangement-invariant function spaces.

I will describe recent work with A. Ferone on the extremals of the Polya-Szego inequality. The inequality says that the $p$-norms of the gradient decrease under symmetrization. It is known that there are non-trivial cases of equality, even when $p>1$. We use Ryff's polar factorization to describe these equality cases.

Speaker's homepage: http://www.math.toronto.edu/almut/

Homotopy Theory

Speaker: Karol Szumilo (Western)

"The Joyal model structure on simplicial sets II"

Time: 13:00

Room: MC 107

I will construct the Joyal model structure.

Colloquium

Speaker: Olivier Haution (Munich)

"p-group actions on smooth projective varieties"

Time: 15:30

Room: MC 107

I will discuss how the geometry of an algebraic variety restricts the possible p-group actions on it, especially concerning fixed points."

Geometry and Topology

Speaker: Karol Szumilo (Western)

"Cofibration Categories and Groupoid $C^*$-algebras"

Time: 15:30

Room: MC 107

I will present a theorem saying that homotopical functors out of a cofibration category are essentially determined by its subcategory of cofibrations. As an application I will discuss a functorial construction of groupoid $C^*$-algebras which is related to the Baum-Connes Conjecture. This is joint work with Markus Land and Thomas Nikolaus.

Analysis Seminar

Speaker: Shengda Hu (Laurier and Waterloo)

"$\mathbb{J}$-holomorphic vector bundles on generalized K\"ahler manifolds"

Time: 15:30

Room: MC 108

Generalized K\"ahler manifold is the analogue of K\"ahler manifold in the framework of generalized geometry \`a la Hitchin. Many non-K\"ahler complex manifolds admit generalized K\"ahler structures. In this context, the analogue of a holomorphic bundle is a $\mathbb{J}$-holomorphic bundle, where $\mathbb{J}$ is one of the generalized complex structures. We will discuss some examples of these objects, a possible candidate for stability and the Kobayashi-Hitchin correspondence in this context.

Speaker's homepage: https://legacy.wlu.ca/homepage.php?grp_id=12368&f_id=43

Homotopy Theory

Speaker: Alex Rolle (Western)

"Coherent Nerve and Simplicial Localization"

Time: 13:00

Room: MC 107

This talk will introduce two new models of infinity categories (simplicially-enriched categories and relative categories), and relate them to quasicategories.

Noncommutative Geometry

Speaker: Babak Beheshti (Western)

"Quantum field theory for mathematicians 1"

Time: 12:30

Room: MC 106

Analysis Seminar

Speaker: Mehdi S. Monfared (Windsor)

"Some results on almost periodic functionals and finite-dimensional representations"

Time: 15:30

Room: MC 108

Almost periodic functions were introduced by Harald Bohr in 1920s as a result of his investigations into the Riemann's zeta function. The theory was further developed by Bochner and von Neumann in the 30s and 40s. An important result of the theory is Bohr-von Neumann approximation theorem stating that trigonometric polynomials are uniformly dense among almost periodic functions.

Bochner's characterization of almost periodicity has been used by Duncan and Ulger (1992) to study almost periodic functionals on Banach algebras. This provides a more general framework to study almost periodicity.

In this talk we discuss some connections between almost periodic functionals and representation theory. Perhaps the simplest connection is that every coordinate functional of a continuous finite-dimensional representation is almost periodic. In the reverse direction, we can show that if $A$ is an involutive Banach algebra, $\pi \colon A \longrightarrow \mathscr L(H)$ is an involutive representation, and $\xi, \eta \in H$ are algebraically cyclic vectors such that the associated coordinate functional $\pi_{\xi, \eta }$ is almost periodic, then $\dim H<\infty$. We also discuss a construction in which one can associate a residually finite-dimensional (RFD) Banach algebra $U(A)$ to a given Banach algebra $A$, and point out its similarities to almost periodic compactification of locally compact groups.

The results in this talk are joint work with M. Filali, from University of Oulu, Finland.

Speaker's homepage: http://web2.uwindsor.ca/math/monfared/Main.html

Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"Random matrix theory learning seminar"

Time: 12:30

Room: MC 106

Homotopy Theory

Speaker: Aji Dhillon (Western)

"Mapping spaces in higher categories (I)"

Time: 13:00

Room: MC 107

The goal of these two talks is to introduce models for mapping spaces in higher categories and show that they are all equivalent. In the process we will discuss straightening and unstraightening, infinity analogue of the Grothendieck construction. We will conclude with a discussion of cartesian fibrations.

Noncommutative Geometry

Speaker: Babak Beheshti (Western)

"Quantum field theory for mathematicians 2"

Time: 11:30

Room: MC 106

Geometry and Topology

Speaker: David Anderson (Ohio State)

"Operational equivariant $K$-theory"

Time: 13:30

Room: MC 107

Given any covariant homology theory on algebraic varieties, the bivariant machinery of Fulton and MacPherson constructs an "operational" bivariant theory, which formally includes a contravariant cohomology component. Taking the homology theory to be Chow homology, this is how the Chow cohomology of singular varieties is defined. I will describe joint work with Richard Gonzales and Sam Payne, in which we study the operational $K$-theory associated to the $K$-homology of $T$-equivariant coherent sheaves. Remarkably, despite its very abstract definition, the operational theory has many properties which make it easier to understand than the $K$-theory of vector bundles or perfect complexes. This is illustrated most vividly by singular toric varieties, where relatively little is known about $K$-theory of vector bundles, while the operational equivariant $K$-theory has a simple description in terms of the fan, directly generalizing the smooth case.

Analysis Seminar

Speaker: Javad Mashreghi (Laval)

"A numerical mapping theorem"

Time: 15:30

Room: MC 108

The spectral mapping theorem is one of the most important results in operator theory. However, the same statement fails for the numerical range. In this talk, we provide several examples to reveal the relation between spectrum and numerical range. Then we discuss a weak version of the spectral mapping theorem that can be extended for the numerical range. This point of view leads us to Halmos conjecture and theorems of Berger-Stampfli and Drury.

Speaker's homepage: https://www.mat.ulaval.ca/departement-et-professeurs/direction-personnel-et-etudiants/professeurs/fiche-de-professeur/show/mashreghi-javad/

Homotopy Theory

Speaker: Aji Dhillon (Western)

"Mapping spaces in higher categories (II)"

Time: 13:00

Room: MC 107

The goal of these two talks is to introduce models for mapping spaces in higher categories and show that they are all equivalent. In the process we will discuss straightening and unstraightening, infinity analogue of the Grothendieck construction. We will conclude with a discussion of cartesian fibrations.

Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"Random Matrix Theory (II)"

Time: 12:30

Room: MC 106

Homotopy Theory

Speaker: Dinesh Valluri (Western)

"Joins, slices, and limits in quasicategories"

Time: 13:00

Room: MC 107

In this talk we will introduce the notions of join, slice, (co)limits in the context of $\infty$-categories. We will also discuss some basic properties relevant to these constructions.

Noncommutative Geometry

Speaker: Sajad Sadeghi (Western)

"A Scalar Curvature Formula for the Noncommutative 3-Torus"

Time: 14:00

Room: MC 104

This talk is based on my joint paper with Masoud Khalkhali and Ali Moatadelro (arXiv:1610.04740). First I will recall Gilkey’s theorem on asymptotic expansion of heat kernels for the special case of Laplacians. I will also introduce the noncommutatvie 3-torus (NCT3) and then I will conformally perturb the standard volume form on it. Then the corresponding perturbed Laplacian will be discussed, and using Connes’ pseudodifferential calculus, I will define the scalar curvature of NCT3. Finally, introducing a rearrangement lemma I will compute an explicit formula for the scalar curvature of the curved noncommutative 3-torus.

Noncommutative Geometry

Speaker: Masoud Khalkhali (Western)

"Random Matrix Theory (III)"

Time: 12:30

Room: MC 107

Geometry and Topology

Speaker: Aji Dhillon (Western)

"Quotient stacks as root stacks"

Time: 15:30

Room: MC 107

Being a root stack imposes strong conditions on inertia groups. Given a group acting on an algebraic variety I will discuss when these conditions are fulfilled and the resulting quotient turns out to be a root stack. This joint work with Ivan Kobyzev uses some fundamental theorems of algebraic geometry, Abhyankar's lemma, the Chevellary-Shephard-Todd theorem and Luna's etale slice theorem. These results will be introduced.

Analysis Seminar

Speaker: Benoit Charbonneau (Waterloo)

"Analytic aspects of the Nahm transform for spatially periodic instantons"

Time: 15:30

Room: MC 108

The study of instantons on the infinite cylinder $\mathbb{R} \times \mathbb{T}^3$ is facilitated by the Nahm transform, a sort of non-linear Fourier transform for connections. Proving that the Nahm transform does what one believes it should do is a task requiring input from geometric analysis and algebraic geometry. This talk focuses on the geometric analysis aspects. This is joint work with Jacques Hurtubise.

Speaker's web page: http://www.math.uwaterloo.ca/~bcharbon/

Homotopy Theory

Speaker: Luis Scoccola (Western)

"Adjoint functors between quasicategories"

Time: 13:00

Room: MC 107

We will generalize the concept of adjoint functors to the theory of quasicategories.