Events by month

Changho Han, Department of Pure Mathematics, University of Waterloo

"A Brief Introduction to the General MMP Part 2"

Continuing from where we left off last time, I will discuss singularities of the MMP. Then, I will give a brief explanation of how the higher-dimensional MMP works; note that there will be some key differences from the surface case, including flips.

This seminar will be held jointly online and in person:

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Not pfaffian, Part II"

James Freitag has shown that the j-function is not Pfaffian using the model theory of differentially closed fields. We will work though his paper, entitled "Not pfaffian".

MC 5417

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets - Part IV"

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 begin on chapter 3.

MC 5403

Michael Albanese, Department of Pure Mathematics, University of Waterloo

"Spin^h and further generalisations of spin"

Robert Martin, University of Manitoba

"Non-commutative measure theory"

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"Spot it! and why it! (works)"

Do you like to play games? Can you easily distinguish different shapes? Are you at least 6 years old? Well then I've got the perfect game for you! It's called Spot it! (or Dobble if you're not from 'Merica). Fundamentally, the game is about quickly spotting the common symbol displayed on a given pair of cards. In this talk we will see the math behind why this game works. Spoiler: it's projective geometry!

Ronnie Nagloo, University of Illinois at Chicago

"Applications of model theory to functional transcendence"

Nicolas Banks, Department of Pure Mathematics, University of Waterloo

"Dual Isogenies, the Weil Pairing, and the Structure of Endomorphism Rings"

We conclude our review of the geometry of elliptic curves by studying dual isogenies. This allows us to prove important results on torsion elements on elliptic curves, culminating in the construction of the Weil pairing and the algebraic structure of rings of isogenies.

MC 5403

Michael Rubinstein, Department of Pure Mathematics, University of Waterloo

"Differential equations related to averages of the k-th divisor function"

Keating, Rodgers, Roditty-Gershon, and Rudnick have given a conjecture for the asymptotic behaviour of the mean square of sums of the $k$-th divisor numbers over short intervals, and have proven formulas for the analogous problem over $\mathbb{F}_q[t]$. I will discuss their work and describe determinantal and differential equations related to their formulas.

Anton Iliashenko, Department of Pure Mathematics, University of Waterloo

"The third Betti number of nearly Kahler 6-manifolds"

Ronnie Nagloo, University of Illinois at Chicago

"Geometric triviality in differentially closed fields"

Matthew Satriano, Department of Pure Mathematics, University of Waterloo

"Toric MMP"

I will discuss the minimal model program for toric varieties.

This seminar will be held jointly online and in person:

Christine Eagles, Department of Pure Mathematics, University of Waterloo

"A Note on Geometric Theories of Fields"

Will Johnson and Jinhe Ye have shown equivalence conditions on expansions of very slim fields, strongly geometric fields and algebraically bounded fields. As a consequence, we get a one-cardinal results for definable sets and positive dimensional interpretable set. We will work though this paper, entitled "A Note on Geometric Theories of Fields".

MC 5417

Keke Zhang, Department of Pure Mathematics, University of Waterloo

"An Introduction to Geometric Langlands"

We will begin with a discussion of the origin of the Langlands program in number theory, which is class field theory. Then we will give an introduction to the geometric Langlands conjecture. We will show Deligne's proof of the simplest case, which is the statement for GL(1).

This seminar will be held both online and in person:

Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo

"The geometry of G2 manifolds: a marriage of non-associative algebra and non-linear analysis"

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Effectively closed sets - Part V"

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 basis theorems and take a brief detour into Martin-Lof randomness.

MC 5403

Rasul Shafikov, Western University

"Lagrangian embeddings, rational convexity, and approximation"

A celebrated theorem of Duval and Sibony characterizes rationally convex real submanifolds in complex Euclidean spaces as those isotropic with respect to a Kahler form. I will discuss how the results in symplectic geometry can be used to obtain some new results in the approximation theory.

MC 5417

Camila Sehnem, Department of Pure Mathematics, University of Waterloo

"C*-envelopes and semigroup C*-algebras"

Patrick Ingram, York University

"Variation of canonical heights in arithmetic dynamics"

Yash Totani, Department of Pure Mathematics, University of Waterloo

"Binary quadratic forms of class number 3"

Upon providing a historical overview of the theory of binary quadratic forms, we talk about the problem of representing positive integers by some specific binary quadratic forms. We will see how the theory of modular forms comes to our rescue.

MC 5403

J.C. Saunders, Middle Tennessee State University

"The Euler Totient Function on Lucas Sequences"

**THIS SEMINAR HAS BEEN POSTPONED TO FEBRUARY 28, 2023**

Paul Cusson, Department of Pure Mathematics, University of Waterloo

"Holomorphic maps between Riemann surfaces"

Rachael Alvir, Department of Pure Mathematics, University of Waterloo

"Scott Complexity"

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"The effective cone for projective horospherical varieties"

I will start working through Brion’s paper “Variétés sphériques et théorie de Mori” on spherical MMP. Specifically, I plan to cover the first half of section 3, with emphasis on horospherical varieties. We should at least see what the cone NE(X) looks like for any projective horospherical variety X.

This seminar will be held jointly online and in person:

Christine Eagles, Department of Pure Mathematics, University of Waterloo

"A Note on Geometric Theories of Fields, Part II"

Will Johnson and Jinhe Ye have shown equivalence conditions on expansions of very slim fields, strongly geometric fields and algebraically bounded fields. As a consequence, we get a one-cardinal results for definable sets and positive dimensional interpretable set. We will work though this paper, entitled "A Note on Geometric Theories of Fields".

MC 5417

Robert Cornea, Department of Pure Mathematics, University of Waterloo

"A basic Introduction to Higgs Bundles and Vafa-Witten Bundles"

Jeremy Champagne, Department of Pure Mathematics, University of Waterloo

The intent of this seminar is to cover some of the basic theory of elliptic curves. Our first objective is to cover chapters 2, 3 and 6 from Joseph Silverman’s book (The Arithmetic of Elliptic Curves). Later in the semester, we will switch our focus towards more specific topics in the theory of elliptic curves.

MC 5403

Thomas Brazelton, University of Pennsylvania

"Equivariant enumerative geometry"

Jason Crann, Carleton University

"Values of quantum non-local games"

Matilde Lalin, University of Montreal

"Sums of the divisor function and random matrix distributions"

The divisor function gives the number of positive divisors of a natural number. How can we go about understanding the behavior of this function when going over the natural numbers? In this talk we will discuss strategies to better understand this function, issues related to the distribution of these values, and connections to the Riemann zeta function and some groups of random matrices.

MC 5501

Javier González Anaya, University of California at Riverside

"Blow-ups of weighted projective planes at a point: Exploring the parameter space of triangles and the MDS property"

Paul Cusson, Department of Pure Mathematics, University of Waterloo

"Holomorphic maps between Riemann surfaces"

Amador Martin-Pizarro, University of Freiburg

"Simplicity of the automorphism group of fields with operators"