An organizational meeting for the Differential Geometry Working Seminar will be held at 2:30pm on January 9, 2024.
M3 4206
Organisational Meeting
We will discuss the format of the seminar and determine the first set of speakers. If you would like to speak or otherwise participate in the meeting and are unable to attend, please contact AJ Fong.
MC 5417
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
Sarah Peluse, University of Michigan
"Arithmetic patterns in dense sets"
Some of the most important problems in combinatorial number theory ask for the size of the largest subset of the integers in an interval lacking points in a fixed arithmetically defined pattern. One example of such a problem is to prove the best possible bounds in Szemerédi's theorem on arithmetic progressions, i.e., to determine the size of the largest subset of {1,...,N} with no nontrivial k-term arithmetic progression x,x+y,...,x+(k-1)y. Gowers initiated the study of higher order Fourier analysis while seeking to answer this question, and used it to give the first reasonable upper bounds for arbitrary k. In this talk, I'll discuss recent progress on quantitative polynomial, multidimensional, and nonabelian variants of Szemerédi's theorem and on related problems in harmonic analysis and ergodic theory.
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