Events

Jesse Peterson, Vanderbilt University

"Amenability and von Neumann algebras"

Amenability for groups is a notion that was first introduced by von Neumann in 1929 in order to provide a conceptual explanation for the Banach-Tarski paradox. The notion has since been exported to many different areas of mathematics and continues to hold a distinguished position in fields such as group theory, ergodic theory, and operator algebras. For von Neumann algebras the notion plays a fundamental role, with the classification of amenable von Neumann algebras by Connes and Haagerup being considered a touchstone of the area. In this talk, I will give a survey of amenability and von Neumann algebras, emphasizing my own contributions related to von Neumann algebras associated with lattices in Lie groups.

MC 5501

Lawrence Mouillé, Syracuse University

"Positive intermediate Ricci curvature with maximal symmetry rank"

The Grove-Searle Maximal Symmetry Rank Theorem (MSRT) is a foundational result in the study of manifolds with positive sectional curvature and large isometry groups. It provides a classification of closed, positively curved manifolds that admit isometric actions by tori of large rank. In this talk, I will present progress towards extending the MSRT to positive intermediate Ricci curvature, a condition that interpolates between positive sectional curvature and positive Ricci curvature. Grove and Searle were able to employ concavity of distance functions to establish their MSRT, but this feature is not available for positive intermediate Ricci curvature. I will discuss how we can overcome this barrier using a strengthening of Wilking's Connectedness Lemma. A portion of this talk is from joint work with Lee Kennard.

MC 5417

Niclas Technau, Max Plank Institute

"Counting Rational Points Near Manifolds"

Choose your favourite, compact manifold M. How many rational points, with denominator of bounded size, are near M? We report on joint work with Damaris Schindler and Rajula Srivastava addressing this question. Our new method reveals an intriguing interplay between number theory, harmonic analysis, and homogeneous dynamics.

MC 5501

Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"Capacity Theory, equilibrium distribution and potential functions"

This is a continuation of the series of talks from the last semester.  This talk will basically follow Chapter 6 of Baker-Rumely's Book: "Potential Theory and Dynamics on the Berkovich Projective Line". We will introduce the Capacity Theory and equilibrium distribution. Then we will study the potential function attached to the equilibrium distribution.

MC 5417

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Computable Structure Theory I"

In this talk we give a basic introduction to computable structure theory. 

MC 5479

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