NUMBER THEORY
November 3, 2021 3:00 pmWe define a generating series of algebraic cycles on the moduli stack of unitary Shtukas and conjecture that it is a Chow-group valued automorphic form. This is a function field...
Read more
NUMBER THEORY
October 27, 2021 3:00 pmThis is a work in progress joint with Daniel Disegni. We formulate a p-adic analogue of the Arithmetic Gan--Gross--Prasad conjecture for unitary groups, relating the p-adic height pairing of the...
Read more
NUMBER THEORY
October 27, 2021 3:00 pmThis is a work in progress joint with Daniel Disegni. We formulate a p-adic analogue of the Arithmetic Gan--Gross--Prasad conjecture for unitary groups, relating the p-adic height pairing of the...
Read more
NUMBER THEORY
October 20, 2021 3:00 pmI will give a finite-time algorithm that, on input (g,K,S) with g > 0, K a totally real number field of odd degree, and S a finite set of places...
Read more
NUMBER THEORY
October 13, 2021 3:00 pmThe étale cohomology of varieties over Q enjoys a Galois action. In the case of Hilbert modular varieties, Nekovář-Scholl observed that this Galois action on the level of cohomology extends...
Read more
SEMINARS, NUMBER THEORY
October 6, 2021 3:00 pmGiven a prime number l, the elliptic modular polynomial of level l is an explicit equation for the locus of elliptic curves related by an l-isogeny. These polynomials have a...
Read more
NUMBER THEORY
September 29, 2021 3:00 pmI will explain a conjecture on density of arithmetic Hodge loci which includes and generalizes several recent density results of these loci in arithmetic geometry. This conjecture has also analogues...
Read more
SEMINARS, NUMBER THEORY
September 22, 2021 3:00 pmGiven a variety over a number field, its geometric etale fundamental group comes equipped with an action of the Galois group. This induces a Galois action on the pro-algebraic completion...
Read more
NUMBER THEORY
September 15, 2021 3:00 pmWe discuss the problem of determining the number of generators and relations of several profinite groups of arithmetic and geometric origin. These include etale fundamental groups of smooth projective varieties,...
Read more
NUMBER THEORY
September 8, 2021 3:00 pmThe p-torsion in the class group of a number field K is conjectured to be small: of size at most |Disc K|^epsilon, and to have constant average size in families...
Read more