In 1982, S. T. Yau conjectured that there exists at least four
embedded minimal 2-spheres in the 3-sphere with an arbitrary
metric. In this talk, we will show that this conjecture holds true
for bumpy metrics and metrics with positive Ricci...
I will discuss the relationship between positive loops of
contactomorphisms of a fillable contact manifold and the symplectic
cohomology (SH) of the filling. The main result is that the
existence of a positive loop which is "extensible" implies
SH...
In this talk, I will first describe how classical Dieudonne
module of finite flat group schemes and p-divisible groups can be
recovered from crystalline cohomology of classifying stacks. Then,
I will explain how in mixed characteristics, using...
Humans tend to be better at physics than at mathematics.
After all, when an apple falls from a tree, there are more
people who can catch it—they know physically how the apple
moves—than people who can compute its trajectory from a
differential...
I will discuss a result with Bonatti and Crovisier from 2009
showing that the C1 generic diffeomorphism f of a closed manifold
has trivial centralizer; i.e. fg = gf implies that g is a power of
f. I’ll discuss features of the C1 topology that enable...
Dimitroglou-Rizell-Golovko constructs a family of Legendrians in
prequantization bundles by taking lifts of monotone Lagrangians.
These lifted Legendrians have a Morse-Bott family of Reeb chords.
We construct a version of Legendrian Contact Homology...
In this talk, I will discuss progress on showing hardness of the
Minimum Circuit Size Problem (MCSP). The computational complexity
of MCSP is a longstanding mystery, dating back as far as Levin's
seminal work on NP-completeness in 1973. Over the...
I will describe the construction of a harmonic measure that
reproduces a harmonic function from its Robin boundary data, which
is a combination of the value of the function and its normal
derivative. I shall discuss the surprising fact that this...