Events

Benoit Charbonneau, Department of Pure Mathematics, University of Waterloo

"Deformed Hermitian-Yang-Mills equation"

The Deformed Hermitian-Yang-Mills equation has been an intense topic of study in the recent past. I will describe the equation, the concept of central charge pertinent in this story, and various conjectures and progress that has been made.

MC 5403

AJ Fong, Department of Pure Mathematics, University of Waterloo

"Affine Schemes"

We will introduce affine schemes, the building blocks of schemes and a generalisation of affine varieties, and discuss the interesting and nontrivial geometry that can happen in them. We will briefly describe some sheaf theory in the process. This talk closely follows section I.1 of Eisenbud-Harris.

MC 5417

Jason Bell, Department of Pure Mathematics, University of Waterloo

"Sparse subsets of the reals"

We look at the first-order theory of the real numbers augmented by a predicate X that is in some natural sense self-similar with respect to a positive integer base. We show that there is a dichotomy: either we can define a Cantor set in our structure or our expansion of the reals is interdefinable with the real numbers augmented by a set of the form {1/r, 1/r^2, 1/r^3, …} for some integer r>=2.  In the latter case, this is equivalent to the structure having NIP and NTP_2.  This is joint work with Alexi Block Gorman.

MC 5479

Changho Han, Department of Pure Mathematics, University of Waterloo

"Extending the torelli map to alternative compactifications of the moduli space of curves"

It is well-known that the Torelli map, that turns a smooth curve of genus g into its Jacobian (a principally polarized abelian variety of dimension g), extends to a map from the Deligne—Mumford moduli of stable curves to the moduli of semi-abelic varieties by Alexeev. Moreover, it is also known that the Torelli map does not extend over the alternative compactifications of the moduli of curves as described by the Hassett—Keel program, including the moduli of pseudostable curves (can have nodes and cusps but not elliptic tails). But it is not yet known whether the Torelli map extends over alternative compactifications of the moduli of curves described by Smyth; what about the moduli of curves of genus g with rational m-fold singularities, where m is a positive integer bounded above? As a joint work in progress with Jesse Kass and Matthew Satriano, I will describe moduli spaces of curves with m-fold singularities (with topological constraints) and describe how far the Torelli map extends over such spaces into the Alexeev compactifications.

MC 5417

Rohini Ramadas, University of Warwick

"Complex dynamics and algebraic geometry"

The field of complex dynamics began in the early 1900s with the study of iterating polynomials with complex coefficients. It gained momentum in the 1980s with important results on the structure of the Mandelbrot set by Douady-Hubbard and others, and connections established by Thurston, Sullivan and others with surface topology and hyperbolic 3-manifolds. The last decade has seen many breakthroughs achieved via new tools from number theory, measure theory and algebraic geometry. I will discuss some of my results, proved via degeneration techniques from algebraic geometry. The talk will highlight the rich interplay between topology on one hand and algebraic geometry/number theory on the other hand.

M3 3127

Uri Bader, The Weizmann Institute

"Cohomology of Arithmetic Groups, Higher Property T and Spectral Gap"

Groups of matrices with integer entries, aka arithmetic groups, are prominent objects of mathematics. From a geometric point of view, they appear as the fundamental groups of locally symmetric space. Topological invariants of such spaces could be seen as group invariants and vice versa. In my talk I will relate this useful link between topology and arithmetics with the theory of unitary representations. More precisely, I will focus on the cohomology of arithmetic groups with unitary coefficients, presenting a recent joint work with Roman Sauer which completely clarifies the theory in small degrees. By the end of the talk I will discuss the relation of the above with the phenomenon of spectral gap and state various related conjectures. I will make an effort to present the subject to a general audience.

MC 5501

Kiseok Yeon, Purdue University

"The Hasse principle for random homogeneous polynomials in thin sets"

In this talk, we introduce a framework via the circle method in order to confirm the Hasse principle for random homogeneous polynomials in thin sets. We first give a motivation for developing this framework by providing an overall history of the problems of confirming the Hasse principle for homogeneous polynomials. Next, we provide a sketch of the proof of our main result and show a part of the estimates used in the proof. Furthermore, by using our recent joint work with H. Lee and S. Lee, we discuss the global solubility for random homogeneous polynomials in thin sets.

Zoom link: https://uwaterloo.zoom.us/j/98937322498?pwd=a3RpZUhxTkd6LzFXTmcwdTBCMWs0QT09

Yash Singh, Department of Pure Mathematics, University of Waterloo

"Chern classes of vector bundles and applications"

We study Chern classes of vector bundles and their connection to grassmanians. We also study the problem of 27 lines on a cubic surface if time permits.

MC 5501

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Computable Structure Theory II"

We will continue our discussion of forcing in computable structure theory.

MC 5479

Adi Glücksam, Northwestern University

"Multi-fractal spectrum of planar harmonic measure"

In this talk, I will define various notions of the multi-fractal spectrum of harmonic measures and discuss finer features of the relationship between them and properties of the corresponding conformal maps. Furthermore, I will describe the role of multifractal formalism and dynamics in the universal counterparts. This talk is based on a joint work with I. Binder.

MC 5501