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DTSTART;TZID=America/Los_Angeles:20191001T121500
DTEND;TZID=America/Los_Angeles:20191001T131000
DTSTAMP:20260503T214259
CREATED:20190824T031500Z
LAST-MODIFIED:20191001T150201Z
UID:1368-1569932100-1569935400@colleges.claremont.edu
SUMMARY:Combinatorics and representation theory of Temperley-Lieb algebras (Zajj Daugherty\, CUNY)
DESCRIPTION:The classical\, one-boundary\, and two-boundary Temperley-Lieb algebras arise in mathematical physics related to solving certain rectangular lattice models.They also have beautiful presentations as “diagram algebras”\, meaning that they have basis elements depicted as certain kinds of graphs\, and multiplication rules are given by stacking diagrams and gluing of vertices. In this talk\, we will explore these algebras and their representation theory\, as well as their relationship to other important diagram algebras in combinatorial representation theory.
URL:https://colleges.claremont.edu/ccms/event/anct-seminar-zajj-daugherty-cuny/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20191008T121500
DTEND;TZID=America/Los_Angeles:20191008T131000
DTSTAMP:20260503T214259
CREATED:20190909T203312Z
LAST-MODIFIED:20190909T203312Z
UID:1495-1570536900-1570540200@colleges.claremont.edu
SUMMARY:Matroids: a unified theory of independence (Mauricio Gomez Lopez\, University of Oregon)
DESCRIPTION:In this talk\, I will give an overview of the theory of matroids. These are mathematical objects which capture the combinatorial essence of linear independence. Besides providing some basic definitions of this theory\, I will discuss several examples of matroids and explain some connections with optimization. Also\, in this talk\, I will introduce matroid polytopes\, which provide a geometric framework for studying matroids. If time permits\, I will discuss some new proofs to known results that I developed with one of my students during a research program this summer.
URL:https://colleges.claremont.edu/ccms/event/matroids-a-unified-theory-of-independence-mauricio-gomez-lopez-university-of-oregon/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20191015T121500
DTEND;TZID=America/Los_Angeles:20191015T131000
DTSTAMP:20260503T214259
CREATED:20190830T203403Z
LAST-MODIFIED:20191010T171535Z
UID:1465-1571141700-1571145000@colleges.claremont.edu
SUMMARY:Sporadic points on modular curves (Ozlem Ejder\, Colorado State University)
DESCRIPTION:A classic and fundamental result in number theory is due to Mordell who proved that the set of points on an elliptic curve defined over a number field forms a finitely generated abelian group; in particular\, it has a finite torsion subgroup. An essential tool to study elliptic curves is the modular curves which are moduli spaces for elliptic curves with an additional structure.  In particular\, $X_1(n)$ classifies the elliptic curves with a point of order of $n$.  Motivated by the classification of torsion problems\, we study the sporadic points on the curve $X_1(n)$\, that is\, the closed points on $X_1(n)$ such that there are at most finitely many points of degree at most $\deg(x)$. In this talk\, we will discuss the finiteness of sporadic points. This is joint with A. Bourdon\, Y. Liu\, F. Odumudu and B. Viray.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-ozlem-ejder-colorado-state-university/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20191029T121500
DTEND;TZID=America/Los_Angeles:20191029T131000
DTSTAMP:20260503T214259
CREATED:20190802T043328Z
LAST-MODIFIED:20190903T050156Z
UID:1347-1572351300-1572354600@colleges.claremont.edu
SUMMARY:Faster point counting for curves over prime power rings (Maurice Rojas\, Texas A&M)
DESCRIPTION:Counting points on algebraic curves over finite fields has numerous applications in communications and cryptology\, and has led to some of the most beautiful results in 20th century arithmetic geometry. A natural generalization is to count the number of points over prime power rings\, e.g.\, the integers modulo a prime power. However\, the theory behind the latter kind of point counting began more recently and there are numerous gaps in our algorithmic knowledge. \nWe give a simple combinatorial construction that reduces point counting over prime power point counting to the prime field case. In particular\, for any bivariate polynomial f in Z[x\,y] and positive integers p and k with p prime\, we show how one can count the number of roots of f in (Z/(p^k))^2 in time p^{1/2 + o(1)} (dk)^{O(1)}\, and even faster for certain curves. This generalizes earlier results of Cheng\, Lecerf\, Saxena\, and Wan in the univariate case\, and simplifies earlier work of Denef\, Igusa\, and Veys on local zeta functions. \nThis is joint work with Caleb Robelle and Yuyu Zhu.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-maurice-rojas-texas-am/
LOCATION:Emmy Noether Room\, Millikan 1021\, Pomona College\, 610 N. College Ave.\, Claremont\, California\, 91711
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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