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...
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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,...
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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...
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NUMBER THEORY
April 28, 2021 3:00 pmThe Rogers-Ramanujan identity is an equality between a certain “q-series” (given as an infinite sum) and a certain modular form (given as an infinite product). Motivated by ideas from physics,...
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NUMBER THEORY
April 21, 2021 3:00 pmThe absolute prismatic site of a p-adic formal scheme carries interesting arithmetic and geometric information attached to the formal scheme. In this talk, after recalling the definition of this site,...
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NUMBER THEORY
April 14, 2021 3:00 pmWe will describe the notion of affine schemes and their modifications in the context of Arakelov geometry. Using geometry of numbers in infinite rank, we will study their cohomological properties....
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NUMBER THEORY
April 7, 2021 3:00 pmThe geometric Satake equivalence due to Lusztig, Drinfeld, Ginzburg, Mirković and Vilonen is an indispensable tool in the Langlands program. Versions of this equivalence are known for different cohomology theories such as...
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NUMBER THEORY
March 24, 2021 3:00 pmI'll discuss 4 different types of integration -- one in the complex setting, one in the tropical setting, and two in the p-adic setting, and the relationships between them. In particular, we...
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NUMBER THEORY
March 17, 2021 3:00 pmFollowing work of Gross-Wallach, Gan-Gross-Savin defined what are called "modular forms" on the split exceptional group G_2. These are a special class of automorphic forms on G_2. I'll review their...
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NUMBER THEORY
March 10, 2021 3:00 pmI'll explain a very simple proof of the fact that K3 surfaces of finite height admit (many) CM lifts, a result due independently to Ito-Ito-Koshikawa and Z. Yang, which was...
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