Algebra / Number Theory / Combinatorics Seminar

Lattice valued vector systems have taken an important role in packing, coding, cryptography, and signal processing problems.  In compressed sensing, improvements in sparse recovery methods can be reached with an additional  assumption that the signal of  interest is lattice  valued, as demonstrated by A.  Flinth  and G. Kutyniok. Equiangular  tight  frames are  particular systems  of […]

Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups of orthogonal matrices: these are called irreducible group frames. Integer spans of rational irreducible group frames form Euclidean lattices with some very nice geometric properties, […]

Given integers $k,l$  and a graph $G$, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges?  The systematic study of this very natural  question  was recently initiated by Alon, Hefetz, Krivelevich and Tyomkyn who also proposed several interesting conjectures on this topic. In this talk we discuss a theorem […]

An agent comes to a fork in a road. There is a sign that says that one of the two roads leads to prosperity and another to death. The agent must take the fork, but she does not know which road leads where. Does the agent have a strategy to get to prosperity? On one […]

Modular forms are ubiquitous in modern number theory.  For instance, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat's Last Theorem.  In addition to number theory, modular forms show up in diverse areas such as coding theory and particle physics.  Roughly speaking, a modular form is a complex-valued […]