School of Mathematics

Let $f: X \to S$ be a quasi-projective family of varieties defined over $\overline{\mathbb{Q}} \subset \mathbb{C}$. We show that the points of $S(\overline{\mathbb{Q}})$ that are Hodge generic for the variation of Hodge structures associated to $f$...

A symplectic manifold $M$ is called tame at infinity if it admits a compatible almost complex structure such that the corresponding Riemannian metric is complete and geometrically bounded. Some such condition is necessary to confine $J$-holomorphic...

The first construction of Ramanujan graphs is due to Lubotzky, Phillips, and Sarnak (STOC 1986, Combinatorica 1987). Their construction and analysis were deeply algebraic, and at the time it seemed that only algebraic methods were strong enough to...

The random geometric graph Geo_d(n,p) is a probability distribution over graphs, constructed by placing n points uniformly on a d-dimensional sphere and connecting two points whenever they are sufficiently close — where the proximity threshold is...

By combining sparse graphs with local constraints, expander codes offer a powerful framework for achieving fast decoding algorithms while maintaining asymptotically good rate and minimum distance. However, the standard constraint-counting arguments...

In the noisy $k$-XOR problem, one is given $y \in \bF_2^\constraints$ and must distinguish between $y$ uniform and $y = A x + e$, where $A$ is the adjacency matrix of a $k$-left-regular bipartite graph with variables and constraints, $x\in \bF_2^...

Contact homeomorphisms are points in the closure of the (compactly supported) contactomorphism group in the homeomorphism group under the C0-topology. Recently, Dimitroglou Rizell and Sullivan showed that the images of closed Legendrians under...

Using Tougeron’s characterization of multisummable (in the positive real directions) series, the latter can be viewed as infinite series of convergent power series with radii of convergence shrinking to 0. In joint work with Jean-Philippe Rolin and...

How does the choice of training data influence an AI model? This question is of central importance to interpretability, privacy, and basic science.  At its core is the data deletion problem: after a reasonable amount of precomputation, quickly...

I will describe recent breakthrough results in multiclass PAC learning that characterize the optimal sample complexity. The talk will discuss recent work of Chirag Pabbaraju, as well as work of Steve Hanneke, Qinglin Meng, Shay Moran, and Amirreza...