webnotice

Francisco Villacis, Department of Pure Mathematics, University of Waterloo

"Pseudo-Gradients and the Smale Condition"

 I will continue the discussion of pseudo-gradients that was started last time. I will talk in short detail about how the topology of the level sets change as we cross critical points of a Morse function and on the stable and unstable manifolds. I will discuss in detail the Smale condition and the space of trajectories of pseudo-gradients with a view towards the construction of the Morse complex.

M3 4206

Talk #1: (1:00pm-2:15pm)

Jing Xuan Chen

"Holomorphic bisectional curvature"

The bisectional curvature on a Kähler manifold (M,J) is defined as H(X,Y)=R(X,JX,JY,Y) for unit vectors X,Y. We will see what we can prove about a compact connected Kähler manifold if we assume that it has positive bisectional curvature.

Talk #2: (2:30pm-4:00pm)

Spiro Karigiannis

"The deTurck trick demystified"

Jesse Madnick, University of Oregon

"Cohomogeneity-One Lagrangian Mean Curvature Flow"

In C^n, mean curvature flow preserves the class of Lagrangian submanifolds, a fact known as "Lagrangian mean curvature flow" (LMCF).  As LMCF typically forms finite-time singularities, it is of interest to understand the blowup models of such singularities, as well as the soliton solutions.

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

Luke MacLean, Department of Pure Mathematics, University of Waterloo

"Reverse Math IV"

In this talk, we will be presenting material from a recent book by Damir Dzhafarov and Carl Mummert. In particular, we will begin on Chapter 4 studying reducibility of problems.

MC 5403

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 "