Adam Humeniuk, Department of Pure Mathematics, University of Waterloo
"A Primer on Topological Data Analysis"
John Dykes, Department of Pure Mathematics, University of Waterloo
"Putting the "Homotopy" in Homotopy Type Theory"
In this week's meeting of the Homotopy Type Theory Seminar, we begin by reviewing path induction. We then interpret Martin-Lof type theory in a homotopy-theoretic manner, viewing types as higher groupoids and functions as functors. We also discuss in detail how the notion of a homotopy between paths is related to identity types. Those who did not attend previous meetings are still encouraged to come!
MC 5413
Rémi Jaoui, Department of Pure Mathematics, University of Waterloo
"Disintegration phenomena for planar algebraic vector fields"
In my talk, I will discuss some disintegration phenomena in the specific case of complex polynomial vector fields on the affine plane \mathbb{A}^2_\mathbb{C}.
Jesse Kass, University of South Carolina
"How to count lines on a cubic surface arithmetically"
Douglas Farenick, University of Regina
"Low-dimensional operator systems, equivalence, and free convexity"
Pranabesh Das, Pure Mathematics, University of Waterloo
"Variants of Erd{\H o}s--Selfridge superelliptic curves and their rational points"
Jairo Goncalves, University of Sao Paulo
"Some problems in division rings"
Let $D$ be a division ring with center $k$ and multiplicative group $D^{\bullet}= D \setminus \{0\}$. Moreover, let $N \vartriangleleft D^{\bullet}$ be a noncentral normal subgroup. We address the various cases in which the following conjecture, due to Lichtman, holds:
Conjecture: $N$ contains a free (non cyclic) subgroup.
Eli Shamovich, Pure Mathematics, University of Waterloo
"Polynomials and rational functions"
Ross Willard, Pure Mathematics, University of Waterloo
"Natural dualities for finitely generated quasi-varieties - definitions and first results"
Rahim Moosa, Pure Mathematics, University of Waterloo
"Pseudo-finite sets and dimension, Part 2"
Having discussed the normalised counting measure on pseudo-finite sets and its application to Szemeredi Regularity, we now introduce the fine and coarse pseudo-finite dimensions for these sets, with an eye toward the Szemerdi-Trotter theorem.