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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

David Meretzky, University of Notre Dame

"A boundedness condition for differential fields"

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

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

Bartlomiej Zawalski, Polish Academy of Sciences

"On affine bodies with rotationally invariant sections"

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

Eric Boulter, Department of Pure Mathematics, University of Waterloo

"Rational points on elliptic curves"

MC 5403

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