Past Events
The monodromy conjecture predicts a relationship between the motivic zeta function of a hypersurface V(f), which governs the number of solutions to f = 0 (mod p^n) if f has integer coefficients and p is a sufficiently large prime, and the eigenvalues of the monodromy action on the cohomology of…
The Pontryagin classes of a real vector bundle can be defined via Chern classes of its complexification, and appear in Hirzebruch's formula for the signature of a smooth 4n-dimensional manifold for example. It was realized long ago that Pontryagin classes can be defined more generally for…
Deletion channels, introduced by Levenshtein in the 60's, are noisy channels that delete bits from the input. A (binary) k-deletion code of length n is a set C of binary strings of length n capable of correcting k such errors, i.e. satisfying the property that …
Index of a Dirac operator; topological invariance of the index; McKean Singer formula; smoothing operators and heat kernels
Solvable Lattice Models Seminar
Abstract: Colored bosonic lattice models were studied and applied by Borodin and Wheeler. We will consider particular bosonic models whose theory is strikingly parallel to the fermionic models described…
Abstract: We discuss the existence and uniqueness (in terms of different boundary conditions) of the infinite-volume Gibbs measure for the Ising model on the integer lattice. The key tool for proving the existence is the FKG inequality. A phase transition arises between the uniqueness and…
The issue is the large time behaviour of a discrete version of the Fisher-KPP equation. While the model has an interest on its own, our long term motivation is to understand the large time dynamics of epidemiological models on graphs.
The main result is…
We will discuss the Poisson behavior of chains of small quadratic non-residues for almost all primes in short intervals. We will begin with some background on quadratic non-residues and then give a brief outline of the proof. This is joint work with Debmalya Basak and Alexandru Zaharescu.