Matthew Satriano, Pure Mathematics, University of Waterloo
"Hodge theory for combinatorial geometries"
Now that we have an overview of the main results of Adiprasito–Huh–Katz, we start going into the details.
MC 5403
Akos Nagy, Department of Pure Mathematics, University of Waterloo
"Seiberg--Witten equation with multiple spinors in dimension 3 --- Part I"
Following Haydys and Walpuski, I will introduce a generalization of the SW equations on 3-manifolds, and prove a compactness theorem for the moduli space of solutions.
In the first talk, I will define the problem (the SW equations with multiple spinors), state the main theorem of the paper, and prove a couple a priori estimates.
M3 3103
Jonny Stephenson, Pure Mathematics, University of Waterloo
"The back-and-forth property and uniform computable categoricity"
Cantor's back-and-forth argument gives a condition allowing one to construct isomorphisms between different copies of mathematical structures by a process of finite extension. We will give a condition which shows when such a procedure can be carried out, as well as demonstrating a link between back-and-forth procedures, effective atomicity, and uniform computable categoricity of structures.
MC 5403
Shubham Dwivedi, Pure Mathematics, University of Waterloo
"The Monotonicity formula"
We will continue our discussion of minimal submanifolds. After discussing some consequences of the First Variation formula, we will state and prove the Monotonicity formula of volume for minimal submanifolds. We will also state (and might prove) the coarea formula.
M3 3103
Sacha Mangerel, University of Toronto
"Some Applications of Pretentiousness in the Theory of Dirichlet Characters"
Ehsaan Hossain, Department of Pure Mathematics, University of Waterloo
"Solvable algebraic groups"
A linear algebraic group is a Zariski-closed group of matrices. We'll study the Lie-Kolchin Theorem that every connected, solvable linear algebraic group G is conjugate to a group of upper-triangular matrices, and see how it is applied to show that $G=N\rtimes T$ where N is a nilpotent group and T is a "maximal torus" in G.
MC 5413
Ertan Elma, Pure Mathematics, University of Waterloo
We will start reading the book 'An Introduction to Sieve Methods and their Applications' by A.C. Cojocaru and M.R. Murty. In this first talk, we will cover some basic results from the first chapter and if time permits we will start Gallagher's 'larger' sieve.
If you are interested in these talks, please send an e-mail to eelma@uwaterloo.ca for some possible time/room changes and for some documents that we may share.
MC 5403
Chris Kottke, New College of Florida
"Compactification of monopole moduli spaces and Sen's conjecture"
Sam Harris, Pure Mathematics, University of Waterloo
"Unitary Correlation Sets"
Anthony McCormick, Department of Pure Mathematics, University of Waterloo
"Nonlinear Spaces of Smooth Maps"
We will discuss the infinite dimensional smooth manifold structure on the space of smooth maps M\to N where M, N are finite dimensional smooth manifolds with M compact.
M3 3103