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DTSTART;TZID=America/Los_Angeles:20260908T121500
DTEND;TZID=America/Los_Angeles:20260908T131000
DTSTAMP:20260821T073419Z
CREATED:20260417T223051Z
LAST-MODIFIED:20260821T073419Z
UID:10001800-1788869700-1788873000@colleges.claremont.edu
SUMMARY:Field extensions built from dynamical systems\, ramification\, and Julia sets (Michelle Manes\, American Institute of Mathematics)
DESCRIPTION:Given a polynomial defined over a field $K$\, you can build an extension of $K_\infty / K$ by adjoining inverse images of some point $\alpha \in K$. The behavior of these extensions (including the degree [K_\infty : K]\, ramification\, and associated Galois representations) are surprisingly different in the cases that $K$ is a number field versus a local field. In this talk\, I’ll describe the development of these ideas over the past almost 20 years\, culminating in some ongoing work that pushes our understanding of the local field case even further and connects these ideas to the (Berkovich) Julia set for the polynomials.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-michelle-manes-american-institute-of-mathematics/
LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20260915T121500
DTEND;TZID=America/Los_Angeles:20260915T131000
DTSTAMP:20260907T173603Z
CREATED:20260830T212148Z
LAST-MODIFIED:20260907T173603Z
UID:10002233-1789474500-1789477800@colleges.claremont.edu
SUMMARY:Kloosterman sums and Bessel functions (Robert Cass\, CMC)
DESCRIPTION:Kloosterman sums are explicit exponential sums which occur in several contexts in number theory and arithmetic geometry. Bessel functions encode a great deal of representation-theoretic information about finite groups of Lie type\, but they are difficult to compute in general. In this talk\, we will carefully define these objects and describe a direct relationship between them. One of our main goals is to provide many explicit examples\, including ones for the exceptional groups E6 and E7.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-robert-cass-cmc-3/
LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20260922T121500
DTEND;TZID=America/Los_Angeles:20260922T131000
DTSTAMP:20260917T215711Z
CREATED:20260917T215711Z
LAST-MODIFIED:20260917T215711Z
UID:10002333-1790079300-1790082600@colleges.claremont.edu
SUMMARY:Hilbert basis for conical semigroups and indecomposable elements (Lenny Fukshansky\, CMC)
DESCRIPTION:The unique minimal generating set for a semigroup of lattice points in an n-dimensional polyhedral cone is called its Hilbert basis. In the case when the cone is spanned by lattice points\, this Hilbert basis is finite\, however its cardinality can be much larger than n. Nevertheless\, a conjecture of Sebö states that each point in this semigroup can be spanned by no more than n elements of the Hilbert basis. We will brief discuss this conjecture and its current status\, and then shift to the situation where the cone in question is the positive orthant in R^n. In this case the Hilbert basis consists of the so-called indecomposable elements\, notation coming from the theory of universal quadratic forms over algebraic number fields. We will classify lattices that have finite versus infinite Hilbert basis of indecomposables. We will then discuss an analogue of Sebö’s conjecture for indecomposables in planar lattices and finish by presenting a counting estimate on the number of indecomposables of bounded norm in this 2-dimensional case. Joint work with Filiana Kostopoulou.
URL:https://colleges.claremont.edu/ccms/event/hilbert-basis-for-conical-semigroups-and-indecomposable-elements-lenny-fukshansky-cmc/
LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20260929T121500
DTEND;TZID=America/Los_Angeles:20260929T131000
DTSTAMP:20260916T004741Z
CREATED:20260916T004741Z
LAST-MODIFIED:20260916T004741Z
UID:10002331-1790684100-1790687400@colleges.claremont.edu
SUMMARY:From the basics of extremal graph theory to bipartite Turan numbers of trees and star forests (Omid Khormali\, HMC)
DESCRIPTION:Extremal graph theory asks how many edges a graph can have while avoiding a given substructure. We will begin with a brief\, accessible introduction to this area\, before turning to a natural variant\, the bipartite Turan number $(m\,n;H)$\, which restricts the host graph to be bipartite. This setting is especially natural when $H$ itself is bipartite\, such as a tree or star forest. We present new results determining the leading-order bipartite Turan number for trees and the exact bipartite Turan number for star forests\, along with a sketch of the key proof ideas.
URL:https://colleges.claremont.edu/ccms/event/from-the-basics-of-extremal-graph-theory-to-bipartite-turan-numbers-of-trees-and-star-forests-omid-khormali-hmc/
LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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