Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"NIP"
We continue to read through Pierre Simon's "A Guide to NIP Theories".
MC 5403
Junichiro Matsuda, Kyoto University
"Algebraic connectedness and bipartiteness of quantum graphs"
Quantum graphs are a non-commutative analogue of classical graphs related to operator algebras, quantum information, quantum groups, etc. In this talk, I will give a brief introduction to quantum graphs and talk about spectral characterizations of properties of quantum graphs. We introduce the notion of connectedness and bipartiteness of quantum graphs in terms of graph homomorphisms, and these properties have algebraic characterizations in the same way as classical cases. We also show the equivalence between bipartiteness and two-colorability of quantum graphs defined by two notions of graph homomorphisms: one respects adjacency matrices, and the other respects edge spaces. This talk is based on arXiv:2310.09500.
This seminar will be held both online and in person:
Akash Sengupta, Department of Pure Mathematics, University of Waterloo
"Chern classes"
We will talk about the definition and basic properties of Chern classes. We will talk about useful techniques for computing Chern classes and discuss how to count lines on a cubic surface.
This seminar will be held both online and in person:
Arul Shankar, University of Toronto
"Secondary terms in the first moment of the 2-Selmer groups of elliptic curves"
Ranks of elliptic curves are often studied via their 2-Selmer groups. It is known that the average size of the 2-Selmer group of elliptic curves is 3, when the family of all elliptic curves is ordered by (naive) height. On the computational side, Balakrishnan, Ho, Kaplan, Spicer, Stein, and Weigand collect and analyze data on ranks, 2-Selmer groups, and other arithmetic invariants of elliptic curves, when ordered by height. Interestingly, they find a persistently smaller average size of the 2-Selmer group in the data. Thus it is natural to ask whether there exists a second order main term in the counting function of the 2-Selmer groups of elliptic curves. In this talk, I will discuss joint work with Takashi Taniguchi, in which we prove the existence of such a secondary term.
MC 5501
We will be streaming the last two lectures of Alain Connes’ Lecture Series titled “From rings of operators to noncommutative geometry” given at the Fields Institute. The lecture series details the origin and impact of non-commutative geometry to various areas in mathematics and will end with recent advances in the program of the operator theoretic approach to the Riemann Hypothesis. Everyone is welcome to join us for a joint viewing experience. For more information and the Zoom link for the first part of the Lecture Series see: http://www.fields.utoronto.ca/activities/23-24/Alain-Connes
MC 5479
Kaleb Ruscitti, Department of Pure Mathematics, University of Waterloo
"Homomorphic Encryption (or: my summer as a Fed)"
In this talk, I will describe homomorphic encryption, which are encryption schemes that allow one to evaluate polynomial functions on the encrypted data. I will introduce the basics of encryption and then the general theory of homomorphic encryption, and then discuss some of the applications to online privacy that I looked at during my summer research internship.
MC 5501
We will be streaming the last two lectures of Alain Connes’ Lecture Series titled “From rings of operators to noncommutative geometry” given at the Fields Institute. The lecture series details the origin and impact of non-commutative geometry to various areas in mathematics and will end with recent advances in the program of the operator theoretic approach to the Riemann Hypothesis. Everyone is welcome to join us for a joint viewing experience. For more information and the Zoom link for the first part of the Lecture Series see: http://www.fields.utoronto.ca/activities/23-24/Alain-Connes
MC 5479
Lucas Mason-Brown, University of Oxford
"Unitary representations of semisimple Lie groups and conical symplectic singularities"
One of the most fundamental unsolved problems in representation theory is to classify the set of irreducible unitary representations of a semisimple Lie group. In this talk, I will define a class of such representations coming from filtered quantizations of certain graded Poisson varieties. The representations I construct are expected to form the "building blocks" of all unitary representations.
MC 5501
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