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...
We discover a surface related to the pair correlation of zeros
of the Riemann zeta function. We make a conjecture on the shape of
the surface and present partial results and numerical evidence
towards the conjecture. This is joint work with Debmalya...
Redshifted 21cm emission from neutral hydrogen is rapidly
becoming one of our most powerful observables in cosmology. With
it, we can study the evolution of dark energy at low/intermediate
redshifts, the epoch of reionization, the first stars in the...
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 prove that the block length of every linear 3-query
Locally Correctable Code (LCC) with a constant distance over any
small field grows exponentially with k, the dimension of the code.
This result gives the first separation between LCCs and...
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...
