Past Events

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving...

Real stable polynomials define real hypersurfaces with special topological structure. These polynomials bound the feasible regions of semidefinite programs and appear in many areas of mathematics, including optimization, combinatorics and...

Let E be an elliptic curve over the rationals. Let K be an imaginary quadratic field and H_K the corresponding Hilbert class field. We discuss recent results on the arithmetic of E over H_K as K varies (joint with H. Hida and Y. Tian).

Supersingular isogeny Diffie-Hellman (SIDH) is an attractive candidate for post-quantum key exchange, in large part due to its relatively small public key sizes. In this work we develop methods to reduce the size of public keys in isogeny-based...

Immune cells are activated when receptors on their surface bind to target pathogenic molecules. This leads to receptor phosphorylation, initiating a cascade of downstream signals. Advances in fluorescence microscopy have made it possible to watch...

Let E be an elliptic curve over the rationals. Let K be an imaginary quadratic field and H_K the corresponding Hilbert class field. We discuss recent results on the arithmetic of E over H_K as K varies (joint with H. Hida and Y. Tian).

We prove two related concentration inequalities concerning the points of elliptic curves contained within subsets of F_p^2. In particular we investigate the probability of a large difference between the portions of quadratic residues and non-residues...

I will report recent progress in De Giorgi's type conjectures (and beyond) for Allen-Cahn equation and some free boundary problems in the whole space.

Many useful and interesting optimization problems can be cast in a convex composite form min_x h(c(x)), where h is a non-smooth but convex function and c is a smooth nonlinear or linear mapping. The non-smoothness of the outer function prevents...

What do toothpaste, paint and glaciers have in common? All three fluids usually behave like a plastic solid, but as soon as the stress exceeds a critical threshold, they suddenly begin to flow like a viscous liquid. Rheologists refer to such...