Alan Talmage, Department of Pure Mathematics, University of Waterloo
"Prime Solutions of Systems of Diagonal Equations"
Talk #1: Jack DeSerrano
"The density of integers n coprime to ⌊αn⌋"
We determine, for a real number α, the density of positive integers n such that gcd(n, ⌊αn⌋) = 1, drawing from a 1953 paper of G. L. Watson. For example, for irrational α, we show that this density is 6/π2.
Talk #2: Owen Sharpe
"Waring's Problem on Function Fields of Characteristic Two"
We review the work of Gallardo and Heath-Brown on Waring's problem in the polynomial rings F_2[t] and F_4[t].
Nicolas Banks, Department of Pure Mathematics, University of Waterloo
"Intersection theory, Chow groups, and a generalized Bezout's Theorem"
Bezout's Theorem is a classical result which states that two plane curves intersect in a number of points equal to the product of their degrees. This theorem has an interesting history: it was essentially known to Newton in the 17th century, while the first proof was attempted a century later by Bezout. The first rigorous, algebro-geometric proof was finally given by Serre in 1958.
Christine Eagles, Department of Pure Mathematics, University of Waterloo
"BABA HAS PROOF"
Talk #1 (1:00-2:30pm): Amanda Petcu
"The G_2 Laplacian flow"
In this talk, we will introduce the G_2 Laplacian flow and attempt to show short-time existence and uniqueness following the work of Bryant and Xu.
Talk #2 (2:30-4:00pm): Sir Michael Atiyah
"A Panoramic View of Mathematics "
Francisco Villacis, Department of Pure Mathematics, University of Waterloo
"Functor of Points and Properties of Schemes"
We will review the functor of points perspective of schemes which was discussed the week of May 29, and we will talk about properties of schemes.
MC 5403
**This talk has been postponed till next week (June 20)**
Francisco Villacis, Department of Pure Mathematics, University of Waterloo
"D-Modules on Smooth Varieties"
In this talk I will talk about D-modules on smooth varieties and the Riemann-Hilbert Correspondence.
MC 5403
Hanming Liu, Department of Pure Mathematics, University of Waterloo
"Introduction"
We will be reading Audin and Damian's book "Morse Theory and Floer Homology". In this introductory talk, I will briefly talk about why symplectic geometers and geometric topologists would want to study Morse theory, and then present chapter 1 and the beginning of chapter 2.
M3 4206
Rahim Moosa, Department of Pure Mathematics, University of Waterloo
"Restricted Zilber Trichotomy"
We will be reading Ben Castle's paper.
MC 4060
Rachael Alvir, Department of Pure Mathematics, University of Waterloo
"Reverse Math III"
In this talk, we will be presenting material from a recent book by Damir Dzhafarov and Carl Mummert. In particular, we will prove the cone avoidance basis theorem.
MC 5403