Events by month

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"Contracting rays in NE(X) for horospherical X"

I will continue with section 3 of Brion’s paper “Variétés sphériques et théorie de Mori”. This time we will start to see how contracting extremal rays of NE(X) affects the coloured fan of X.

This seminar will be held jointly online and in person:

Jenny Xu, Department of Pure Mathematics, University of Waterloo

"An Invitation to Model-Theoretic Galois Theory (Part I)"

Robert Cornea, Department of Pure Mathematics, University of Waterloo

A basic Introduction to Higgs Bundles and Vafa-Witten Bundles, Part Two

Gian Cordana Sanjaya, Department of Pure Mathematics, University of Waterloo

"Elliptic Curves"

We switch our discussion to elliptic curves over finite fields. We prove Hasse’s bound and Weil conjecture, and we discuss more structures on elliptic curves over finite fields.

MC 5403

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets - Part VI"

An effectively closed set (or $\Pi^0_1$ class) in Baire space $\omega^\omega$ is the set $[T]$ of infinite branches through a computable tree $T$. This semester in the computability seminar, we will be studying $\Pi^0_1$ classes from Cenzer \& Remmel's textbook. This week we will start proving an effective version of the perfect set theorem.

MC 5403

Scott Wilson, City University of New York

"Homotopical obstructions to the existence of certain complex structures on smooth manifolds"

Jintao Deng, Department of Pure Mathematics, University of Waterloo

"The K-theory of relative group C*-algebras"

Amanda Petcu, Department of Pure Mathematics, University of Waterloo

"A History of Women in Math"

Xingchi Ruan, Department of Pure Mathematics, University of Waterloo

"Singular Series in the Hilbert-Kamke Problem"

The Hilbert-Kamke problem is a well-known problem in number theory. It looks for the solubility of a certain type of system of equations. We talk about how the singular series will provide solubility to the Hilbert-Kamke problem, and we will find a lower bound of the number of variables to ensure the sum of the singular series is positive.

MC 5403

Liam Orovec, Department of Pure Mathematics, University of Waterloo

"Unique Representations of Real Numbers in Non-Integer Bases"

Eric Boulter, Department of Pure Mathematics, University of Waterloo

"Co-isotropic foliations in holomorphic symplectic manifolds"

Natasha Dobrinen, University of Notre Dame

"Infinite-dimensional Ramsey theory for binary relational free amalgamation classes"

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"Contracting the other rays in NE(X) for horospherical X"

I plan to continue from last time on contracting extremal rays in NE(X). This time, we will see how to contract the curve classes coming from walls in the coloured fan for X. So the plan is to touch on section 3.6 and then move to section 4.6 in Brion’s paper “Variétés sphériques et théorie de Mori”. If there is time, I will start the other material in section 4: flips.

Jenny Xu, Department of Pure Mathematics, University of Waterloo

"An Invitation to Model-Theoretic Galois Theory (Part II)"

Xiao Zhong, Department of Pure Mathematics, University of Waterloo

"Dynamical Cancellation of Polynomials"

Yash Singh, Department of Pure Mathematics, University of Waterloo

"Supersingular reduction of elliptic curves"

We study reductions of elliptic curves modulo p and the phenomenon of supersingular reductions. Time permitting, we will prove a landmark theorem of Elkies in this vein.

MC 5403

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Metatheorems"

Luca Di Cerbo, University of Florida

"Complex structures on 4-manifolds"

Yuming Zhao, Department of Pure Mathematics, University of Waterloo

"An operator algebraic formulation of self-testing"

Dan Christensen, Western University

"An introduction to homotopy type theory"

Sourabh Das, Department of Pure Mathematics, University of Waterloo

"An explicit version of Chebotarev's density theorem"

Matthew Satriano, Department of Pure Mathematics, University of Waterloo

"Galois closures and components of Hilbert schemes"

Michael Albanese, Department of Pure Mathematics, University of Waterloo

"The Hitchin-Thorpe Inequality"

Alexi Block Gorman, McMaster University

"Toward a characterization of V_k-definability"

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"Flipping horospherical varieties"

(the title should be read in John Sawatzky’s voice). In what is likely the final talk of the seminar, we will see how flips work in the context of MMP on horospherical varieties. This is following section 4 of Brion’s paper “Variétés sphériques et théorie de Mori”.

This seminar will be held jointly online and in person:

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Uncollapsed Hrushovski constructions"

Hrushovski constructions have been used to construct many counterexamples in model theory, and also have interactions with combinatorics. In their uncollapsed, infinite rank form, they are very similar to the classical Fraisse limits. I will go through the basic properties of uncollapsed Hrushovski constructions, following David Evan's note "An introduction to ampleness".

MC 5417

Ruxandra Moraru, Department of Pure Mathematics, University of Waterloo

"Deformation theory of vector bundles and of Hitchin pairs"

Eric Boulter, Department of Pure Mathematics, University of Waterloo

"Rational points on elliptic curves"

MC 5403

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Even More Effectively Closed Sets"

An effectively closed set (or $\Pi^0_1$ class) in Baire space $\omega^\omega$ is the set $[T]$ of infinite branches through a computable tree $T$. This semester in the computability seminar, we will be studying $\Pi^0_1$ classes from Cenzer \& Remmel's textbook. This week we will continue proving an effective version of the perfect set theorem.

MC 5403

Lisa Marquand, Stony Brook University

"Symplectic Birational Involutions of manifolds of OG10 type"

Roberto Hernandez Palomares, Department of Pure Mathematics, University of Waterloo

"K-theoretic classification of inductive limit actions of fusion categories on AF C*-algebras"

Jason Lotay, Oxford University

"Minimal Lagrangians and where to find them"

Note: The time of this talk is different from the usual Number Theory Seminar time.

Trevor Wooley, Purdue University

"Waring's problem and Freiman's theorem"

Christopher Lang, Department of Pure Mathematics, University of Waterloo

"Hyperbolic monopoles with continuous symmetries (part 2)"

Few examples of hyperbolic monopoles exist. By modifying previous work of mine with collaborators, we will discuss a structure theorem for generating highly symmetric hyperbolic monopoles. We will briefly cover general geometric details discussed in my previous talk and focus more on the use of representation theory to generate monopoles and examine some examples generated by the method.

MC 5403

David Meretzky, University of Notre Dame

"A boundedness condition for differential fields"

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Uncollapsed Hrushovski constructions, part 2"

Last week, we constructed the Hrushovski-Fraisse limit of a class of finite relational structures. This week, I will axiomatize these limits and prove they are omega-stable. I will also give a characterization of forking. If time allows, I will show some potential application. 

MC 5417

Francisco Villacis, Department of Pure Mathematics, University of Waterloo

"Integrable System on Smooth Projective Toric Varieties, Part 2"

This is a continuation to my previous talk on building an integrable system on smooth projective toric varieties. In my previous talk, I explained how to view a smooth projective toric variety as a symplectic reduction. In this talk I will briefly review this construction and from here show that the torus action in our variety is Hamiltonian and explain how the integrable system is constructed.

Maya Gusak, University of Waterloo

"Elliptic Curve Cryptography"

MC 5403

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Metatheorems (Part 2)"

We will introduce the game metatheorem of Antonio Montalban and discuss its function. Several examples of its usefulness will be given.

MC 5403

Alexander Yampolsky, V.N. Karazin National University, Kharkiv, Ukraine

"Some aspects of geometry of unit vector fields"

Bartlomiej Zawalski, Polish Academy of Sciences

"On affine bodies with rotationally invariant sections"

Guoliang Yu, Texas A&M University

"Index theory of the Dirac operator on manifolds with polyhedral boundary and its applications"

I will introduce a new index theory for Dirac operators on manifolds with polyhedral boundary and discuss how this theory can be applied to solve Gromov's dihedral extremality conjecture on scalar curvature. This is joint work with Jinmin Wang and Zhizhang Xie. This talk will be accessible to non-experts including graduate students.

MC 5501

Cameron Stewart, Department of Pure Mathematics, University of Waterloo

"On prime factors of binary recurrence sequences"

We shall discuss estimates for the greatest prime factor of terms of binary recurrence sequences.

MC 5479

William Gollinger, University of Waterloo

"Four" proofs that \pi_1(G) is abelian

Lucia Martin Merchan, Department of Pure Mathematics, University of Waterloo

"Formality of Joyce's manifolds"

Salma Shaheen, Department of Pure Mathematics, University of Waterloo

"Algebras from Finite Group Actions"

Christine Eagles, Department of Pure Mathematics, University of Waterloo

"Domination in stable theories"

Keke Zhang, Department of Pure Mathematics, University of Waterloo

"More about the Langlands Program"

We will talk about the Fourier-Mukai transform and how it relates to geometric Langlands correspondence, Geometric Langlands for reductive groups (geometric Satake equivalence) and their examples. If time allows, we will give a deformed version of the Fourier-Mukai transform.

This seminar will be held both online and in person:

Nic Banks, Department of Pure Mathematics, University of Waterloo

"The inverse Galois problem"

MC 5403

Aleksandar Milivojevic, Max Planck Institute for Mathematics, Bonn

"Topological aspects of almost complex structures on the six sphere"

Paul Skoufranis, York University

"An Overview of Free and Bi-Free Probability"

In this talk, we will provide an overview of the definitions, structures, examples, results, and applications in free probability and its recent generalization known as bi-free probability.

This seminar will be held both online and in person: