Video Lectures

The tangent bundle of a Kähler manifold admits in a neighborhood of the zero section a hyperkähler structure. From a symplectic point of view, this means we have three symplectic structures all compatible with a single metric. Two of the three...

The online discrepancy minimization problem asks, given unit vectors v_1, ..., v_t arriving one at a time, for online signs x_1 ..., x_t4 in {-1, 1} so that the signed sum x_1 v_1 + ... + x_t v_t has small coordinates in absolute value.

In the first...

Because of the existence of approximate p-power roots, a perfectoid algebra over Q_p admits no continuous derivations, and thus the natural Kahler tangent space of a perfectoid space over Q_p is identically zero. However, it turns out that many...

A function f:𝔽n2→𝔽n2 is linear if f(x+y)=f(x)+f(y) for all pairs (x,y).

Suppose f is "a bit linear" -- say, f(x+y)=f(x)+f(y) for 1% of pairs(x,y).  Must f agree with a truly linear function a positive proportion of the time?  How large a proportion...

I will discuss a recursive formula for the homotopy type of the space of Legendrian embeddings of sufficiently positive cables with the maximal Thurston-Bennequin invariant. Via this formula, we identify infinitely many new components within the...

Lagrangian cobordisms induce exact triangles in the Fukaya category. But how many exact triangles can be recovered by Lagrangian cobordisms? One way to measure this is by comparing the Lagrangian cobordism group to the Grothendieck group of the...

In the talk, I will introduce a distance-like function on the zero section of the cotangent bundle using symplectic embeddings of standard balls inside an open neighborhood of the zero section. I will provide some examples which illustrate the...