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DTSTART;TZID=America/Los_Angeles:20190430T121500
DTEND;TZID=America/Los_Angeles:20190430T131000
DTSTAMP:20260529T174915
CREATED:20190123T071945Z
LAST-MODIFIED:20190419T172528Z
UID:1149-1556626500-1556629800@colleges.claremont.edu
SUMMARY:What Did Ada Do? Digging into the Mathematical Work of Ada Lovelace (Gizem Karaali\, Pomona)
DESCRIPTION:Augusta Ada Byron King Lovelace (1815-1852) is today celebrated as the first computer programmer in history. This might be confusing to some because in 1852 there were no machines that looked like what we call computers today. In this talk I attempt to explain what Ada really did\, and delineate the mathematics involved. Bernoulli numbers will definitely come into play\, but there may also be other fun distractions along the way\, possibly including some juicy gossip about Ada’s life.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-gizem-karaali-pomona/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190423T121500
DTEND;TZID=America/Los_Angeles:20190423T131000
DTSTAMP:20260529T174915
CREATED:20190312T201357Z
LAST-MODIFIED:20190312T201357Z
UID:1273-1556021700-1556025000@colleges.claremont.edu
SUMMARY:Theory of vertex Ho-Lee-Schur graphs (Sin-Min Lee\, SJSU)
DESCRIPTION:A triple of natural numbers (a\,b\,c) is an S-set if a+b=c. I. Schur used the S-sets to show that for n >3\, there exists s(n) such that for prime p > s(n)\, x^p + y^p = z^p (mod p) has a nontrivial solution. A (p\,q)-graph G is said to be vertex Ho-Lee-Schur graph if there exists a bijection f: V(G) –> {1\,2\,…\,p} such that for each C3 subgraph of G with vertices {x\,y\,z} the triple (f(x)\,f(y)\,f(z)) is an S-set. The VHLS deficiency of G is the smallest k such that GU Nk\, where Nk is null graph\,  is a vertex Ho-Lee-Schur graph. We determine VHLS deficiency of some graphs and show that no Kuratowski type characterization of non-vertex Ho-Lee-Schur graphs. Some relation of integer partitions and this theory  is explored. We will also introduce some unsolved problems and invite the audience to  solve them.
URL:https://colleges.claremont.edu/ccms/event/theory-of-vertex-ho-lee-schur-graphs-sin-min-lee-sjsu/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190416T121500
DTEND;TZID=America/Los_Angeles:20190416T131000
DTSTAMP:20260529T174915
CREATED:20190123T071749Z
LAST-MODIFIED:20190408T231144Z
UID:1147-1555416900-1555420200@colleges.claremont.edu
SUMMARY:Chow rings of heavy/light Hassett spaces via tropical geometry (Dagan Karp\, HMC)
DESCRIPTION:In this talk\, I will try to give a fun introduction to tropical geometry and Hassett spaces\, and show how tropical geometry can be used to compute the Chow rings of Hassett spaces combinatorially. This is joint work with Siddarth Kannan and Shiyue Li.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-dagan-karp-hmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190409T121500
DTEND;TZID=America/Los_Angeles:20190409T131000
DTSTAMP:20260529T174915
CREATED:20190123T071619Z
LAST-MODIFIED:20190402T034536Z
UID:1145-1554812100-1554815400@colleges.claremont.edu
SUMMARY:Matrix multiplication: the hunt for $\omega$ (Mark Huber\, CMC)
DESCRIPTION:For centuries finding the determinant of a matrix was considered to be something that took $\Theta(n^3)$ steps.  Only in 1969 did Strassen discover that there was a faster method.  In this talk I’ll discuss his finding\, how the Master Theorem for divide-and-conquer plays into it\, and how it was shown that finding determinants\, inverting matrices\, and Gaussian elimination are the same time complexity as to matrix multiplication.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-mark-huber-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190402T121500
DTEND;TZID=America/Los_Angeles:20190402T131000
DTSTAMP:20260529T174915
CREATED:20190206T180617Z
LAST-MODIFIED:20190326T042503Z
UID:1196-1554207300-1554210600@colleges.claremont.edu
SUMMARY:Fibonacci and Lucas analogues of binomial coefficients and what they count (Curtis Bennett\, CSULB)
DESCRIPTION:A Fibonomial is what is obtained when you replace each term of the binomial coefficients $ {n \choose k}$ by the corresponding Fibonacci number.  For example\, the Fibonomial \n$${ 6\brace 3 } = \frac{F_6 \cdot F_5 \cdot \dots \cdot F_1}{(F_3\cdot F_2 \cdot F_1)(F_3\cdot F_2 \cdot F_1)} = \frac{8\cdot5\cdot3\cdot2\cdot1\cdot1}{(2\cdot1\cdot1)(2\cdot1\cdot1)} = 60$$ \nsince the first six Fibonacci numbers are 1\, 1\, 2\, 2\, 5\, and 8.  Curiously the Fibonomials are always integers\, raising the combinatorial question:  what do they count?  In this talk we introduce and provide a little history of the Fibonomials.  We then provide a simple object the Fibonomials enumerate.  We will use this new object to prove various Fibonomial analogues of standard identities on binomial coefficients and discuss further generalizations including the Lucanomials.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-curtis-bennett-csulb/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190326T121500
DTEND;TZID=America/Los_Angeles:20190326T131000
DTSTAMP:20260529T174915
CREATED:20190224T030836Z
LAST-MODIFIED:20190304T190113Z
UID:1236-1553602500-1553605800@colleges.claremont.edu
SUMMARY:Refinements of metrics (Wai Yan Pong\, CSUDH)
DESCRIPTION:I will talk about a few graph-theoretic metrics then introduce the concept of refinements on a class of functions that include all metrics. As a case study\, we will construct various refinements on the shortest-path distance. Consequently\, we obtain a few “better” versions of the Erdos number. In the course of our investigation\, we realized various construction of metrics can be unified under a rather natural concept that we called monotonic monoid norm. This is a joint work with Kayla Lock and Alex Wittmond.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-wai-yan-pong-csudh/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190312T121500
DTEND;TZID=America/Los_Angeles:20190312T131000
DTSTAMP:20260529T174915
CREATED:20181221T200102Z
LAST-MODIFIED:20181221T232930Z
UID:991-1552392900-1552396200@colleges.claremont.edu
SUMMARY:Indiana Pols Forced to Eat Humble Pi: The Curious History of an Irrational Number (Edray Goins\, Pomona)
DESCRIPTION:In 1897\, Indiana physician Edwin J. Goodwin believed he had discovered a way to square the circle\, and proposed a bill to Indiana Representative Taylor I. Record which would secure Indiana’s the claim to fame for his discovery.  About the time the debate about the bill concluded\, Purdue University professor Clarence A. Waldo serendipitously came across the claimed discovery\, and pointed out its mathematical impossibility to the lawmakers.  It had only be shown just 15 years before\, by the German mathematician Ferdinand von Lindemann\, that it was impossible to square the circle because $\pi$ is an irrational number.  This fodder became ignominiously known as the “Indiana Pi Bill” as Goodwin’s result would force $\pi = 3.2$.\n\nIn this talk\, we review this humorous history of the irrationality of $\pi$.  We introduce a method to compute its digits\, present Lindemann’s proof of its irrationality (following a simplification by Miklos Laczkovich)\, discuss the relationship with the Hermite-Lindemann-Weierstrass theorem\, and explain how Edwin J. Goodwin came to his erroneous conclusion in the first place.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-edray-goins-pomona/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190305T121500
DTEND;TZID=America/Los_Angeles:20190305T131000
DTSTAMP:20260529T174915
CREATED:20190123T071437Z
LAST-MODIFIED:20190227T165818Z
UID:1143-1551788100-1551791400@colleges.claremont.edu
SUMMARY:Nonvanishing minors and uncertainty principles for Fourier analysis over  finite fields (Daniel Katz\, CSUN)
DESCRIPTION:Chebotarev’s theorem on roots of unity says that every minor of a discrete Fourier transform matrix of prime order is nonzero. We present a generalization of this result that includes analogues for discrete cosine and discrete sine transform matrices as special cases.  This leads to a generalization of the Biro-Meshulam-Tao uncertainty principle to functions with symmetries that arise from certain group actions\, with some of the simplest examples being even and odd functions.  This new uncertainty principle gives a bound that is sharp and\, for some classes of functions\, stronger than that of Biro-Meshulam-Tao.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-csun/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190226T121500
DTEND;TZID=America/Los_Angeles:20190226T131000
DTSTAMP:20260529T174915
CREATED:20190112T015039Z
LAST-MODIFIED:20190218T190711Z
UID:1047-1551183300-1551186600@colleges.claremont.edu
SUMMARY:When is the product of Siegel eigenforms an eigenform? (Jim Brown\, Occidental College)
DESCRIPTION:Modular forms are ubiquitous in modern number theory.  For instance\, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat’s Last Theorem.  In addition to number theory\, modular forms show up in diverse areas such as coding theory and particle physics.  Roughly speaking\, a modular form is a complex-valued function defined on the complex upper half-plane that satisfies a large number of symmetries.  A modular form has two invariants: weight and level.  If one fixes a weight and level\, the collection of modular forms of that weight and level form a finite-dimensional complex vector space.  One has a collection of operators on these spaces referred to as Hecke operators.  A natural question is if one takes two eigenforms of these operators and multiplies them\, when is the product still an eigenform?  It was shown in independent work by Duke and Ghate that there is a finite list of pairs of eigenforms whose product is again an eigenform.  In this talk we will report on the case when one replaces modular forms with the more general case of Siegel modular forms.  This is work that was partially conducted during an REU in summer 2018.  No prior familiarity with modular forms is assumed.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-jim-brown-occidental-college/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190219T121500
DTEND;TZID=America/Los_Angeles:20190219T131000
DTSTAMP:20260529T174915
CREATED:20190123T071222Z
LAST-MODIFIED:20190203T022044Z
UID:1141-1550578500-1550581800@colleges.claremont.edu
SUMMARY:Knowledge\, strategies\, and know-how (Pavel Naumov\, CMC)
DESCRIPTION:An agent comes to a fork in a road. There is a sign that says that one of the two roads leads to prosperity and another to death. The agent must take the fork\, but she does not know which road leads where. Does the agent have a strategy to get to prosperity? On one hand\, since one of the roads leads to prosperity\, such a strategy clearly exists. On the other\, the agent does not know what the strategy is. \nIf a coalition of agents has a strategy\, it knows that it has a strategy\, and it also knows what this strategy is\, then we say that the coalition has a know-how strategy. In this talk I will discuss several of my recent papers on modal logics that describe the interplay between coalition knowledge\, strategies\, and know-how strategies.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-pavel-naumov-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190212T121500
DTEND;TZID=America/Los_Angeles:20190212T131000
DTSTAMP:20260529T174915
CREATED:20181227T132155Z
LAST-MODIFIED:20190120T184543Z
UID:994-1549973700-1549977000@colleges.claremont.edu
SUMMARY:Subgraph statistics (Benny Sudakov\, ETH Zurich)
DESCRIPTION:Given integers $k\,l$  and a graph $G$\, how large can be the fraction of $k$-vertex subsets of $G$ which span exactly $l$ edges?  The systematic study of this very natural  question  was recently initiated by Alon\, Hefetz\, Krivelevich and Tyomkyn who also proposed several interesting conjectures on this topic. \n\nIn this talk we discuss a theorem which proves one of their conjectures and implies an asymptotic version of another.  We also make some first steps towards analogous question for hypergraphs. Our proofs involve some Ramsey-type arguments\, and a number of different probabilistic tools\, such as polynomial anticoncentration inequalities and  hypercontractivity. \nJoint work with M. Kwan and T. Tran.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-benny-sudakov-eth-zurich/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190205T121500
DTEND;TZID=America/Los_Angeles:20190205T131000
DTSTAMP:20260529T174915
CREATED:20181205T171033Z
LAST-MODIFIED:20190123T223504Z
UID:963-1549368900-1549372200@colleges.claremont.edu
SUMMARY:Lattices from group frames and vertex transitive graphs (Lenny Fukshansky\, CMC)
DESCRIPTION:Tight frames in Euclidean spaces are widely used convenient generalizations of orthonormal bases. A particularly nice class of such frames is generated as orbits under irreducible actions of finite groups of orthogonal matrices: these are called irreducible group frames. Integer spans of rational irreducible group frames form Euclidean lattices with some very nice geometric properties\, called strongly eutactic lattices. We discuss this construction\, focusing on an especially interesting infinite family in arbitrarily large dimensions\, which comes from vertex transitive graphs. We demonstrate several examples of such lattices from graphs that exhibit some rather fascinating properties. This is joint work with D. Needell\, J. Park and J. Xin.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-lenny-fukshansky-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190129T121500
DTEND;TZID=America/Los_Angeles:20190129T131000
DTSTAMP:20260529T174915
CREATED:20181130T222530Z
LAST-MODIFIED:20181130T222530Z
UID:961-1548764100-1548767400@colleges.claremont.edu
SUMMARY:Discrete compressed sensing: lattices and frames (Josiah Park\, Georgia Tech)
DESCRIPTION:Lattice valued vector systems have taken an important role in packing\, coding\, cryptography\, and signal processing problems.  In compressed sensing\, improvements in sparse recovery methods can be reached with an additional  assumption that the signal of  interest is lattice  valued\, as demonstrated by A.  Flinth  and G. Kutyniok. Equiangular  tight  frames are  particular systems  of unit  vectors  with minimal  coherence\,  a measure of how well distributed the vectors are\, and have provable guarantees for recovery of sparse vectors in standard methods.  The determination whether real equiangular tight frames have integer span on a lattice has been given a characterization within two papers by A. Bottcher\, L. Fukshansky\, one with S. R. Garcia\, H. Maharaj and D. Needell.  Here the corresponding question is considered for the complex case and several families are demonstrated to have either integer span on a lattice or not.  In addition\, it is demonstrated that a real Parseval tight frame can have integer span on a lattice if and only if the inner products appearing in the system are rational.  (Collaboration with L. Fukshansky\, D. Needell\, and Y. Xin)
URL:https://colleges.claremont.edu/ccms/event/discrete-compressed-sensing-lattices-and-frames-josiah-park-georgia-tech/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190122T121500
DTEND;TZID=America/Los_Angeles:20190122T131000
DTSTAMP:20260529T174915
CREATED:20190112T013635Z
LAST-MODIFIED:20190113T053629Z
UID:1045-1548159300-1548162600@colleges.claremont.edu
SUMMARY:Niebrzydowski tribrackets and algebras (Sam Nelson\, CMC)
DESCRIPTION:In this talk we will survey recent work on Niebzydowski Tribrackets and Niebrydowski Algebras\, algebraic structures related to region colorings the planar complements of knots and trivalent spatial graphs.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sam-nelson-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181211T121500
DTEND;TZID=America/Los_Angeles:20181211T131000
DTSTAMP:20260529T174915
CREATED:20181017T000951Z
LAST-MODIFIED:20181205T171813Z
UID:915-1544530500-1544533800@colleges.claremont.edu
SUMMARY:The Bateman—Horn conjecture II:  applications (Stephan Garcia\, Pomona)
DESCRIPTION:We begin with a review of the Bateman—Horn conjecture\, which sheds light on the intimate relationship between polynomials and prime numbers.  In this expository talk\, we survey a host of applications of the conjecture.  For example\, Landau’s conjecture\, the twin prime conjecture\, and the Green—Tao theorem are all consequences of the Bateman—Horn conjecture.  Moreover\, the conjecture also illuminates the mysterious patterns observed in the Ulam spiral.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-stephan-garcia-pomona/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181204T121500
DTEND;TZID=America/Los_Angeles:20181204T131000
DTSTAMP:20260529T174915
CREATED:20180817T150812Z
LAST-MODIFIED:20181116T225428Z
UID:441-1543925700-1543929000@colleges.claremont.edu
SUMMARY:Sperner's lemma: generalizations and applications (Oleg Musin\, UT Rio Grande Valley)
DESCRIPTION:The classical Sperner –  KKM (Knaster – Kuratowski – Mazurkiewicz) lemma has many applications  in combinatorics\, algorithms\, game theory and mathematical economics. In this talk we consider generalizations of this lemma as well as Gale’s colored KKM lemma and Shapley’s KKMS theorem. It is shown that spaces and covers can be much more general and the boundary KKM rules can be substituted by more weaker boundary assumptions. These generalizations of Sperner’s lemma rely on homotopy invariants of covers  that in fact are obstructions for extending a cover of a subspace A in X to a cover of  X.
URL:https://colleges.claremont.edu/ccms/event/tba-2/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181127T121500
DTEND;TZID=America/Los_Angeles:20181127T131000
DTSTAMP:20260529T174915
CREATED:20181002T061007Z
LAST-MODIFIED:20190115T082646Z
UID:892-1543320900-1543324200@colleges.claremont.edu
SUMMARY:Weil sums of binomials: properties and applications (Daniel Katz\, CSUN)
DESCRIPTION:We consider sums in which an additive character of a finite field F is applied to a binomial whose individual terms (monomials) become permutations of F when regarded as functions.  These Weil sums characterize the nonlinearity of power permutations of interest in cryptography.  They also tell us about the correlation of linear recursive sequences over finite fields that are used in digital communications and remote sensing.  In these applications\, one is interested in the spectrum of Weil sum values that are obtained as the coefficients in the binomial are varied.  We discuss topics of enduring interest: Archimedean and non-Archimedean bounds on the sums\, the number of values in the spectrum\, and the presence or absence of zero in the spectrum.  We indicate some important open problems and discuss progress that has been made on them.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-talk-by-daniel-katz-csun/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181113T121500
DTEND;TZID=America/Los_Angeles:20181113T131000
DTSTAMP:20260529T174915
CREATED:20180912T174329Z
LAST-MODIFIED:20181105T225953Z
UID:551-1542111300-1542114600@colleges.claremont.edu
SUMMARY:Cayley digraphs of matrix rings over finite fields (Yesim Demiroglu\, HMC)
DESCRIPTION:In this talk we use the unit-graphs and the special unit-digraphs on matrix rings to show that every n x n nonzero matrix over F_q can be written as a sum of two SL_n-matrices when n>1. We compute the eigenvalues of these graphs in terms of Kloosterman sums and study their spectral properties; and prove that if X is a subset of Mat_2 (F_q) with size |X| > (2 q^3 \sqrt{q})/(q – 1)\, then X contains at least two distinct matrices whose difference has determinant $\alpha$ for any $\alpha \in F_q^*$. Using this result we also prove a sum-product type result: if $A\,B\,C\,D \subseteq F_q$ satisfy $\sqrt[4]{|A||B||C||D|}= \Omega (q^{0.75})$ as q tends to infinity\, then $(A – B)(C – D)$ equals all of $F_q$. In particular\, if A is a subset of F_q with cardinality $|A| > \frac{3}{2} q^{3/4}$\, then the subset $(A – A) (A – A)$ equals all of $F_q$. We also recover a classical result: every element in any finite ring of odd order can be written as the sum of two units. This talk should be accessible to undergraduates with some background in linear algebra.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-yesim-demiroglu-hmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181106T121500
DTEND;TZID=America/Los_Angeles:20181106T131000
DTSTAMP:20260529T174915
CREATED:20180911T214141Z
LAST-MODIFIED:20181102T201125Z
UID:537-1541506500-1541509800@colleges.claremont.edu
SUMMARY:Turning probability into polynomials (Mark Huber\, CMC)
DESCRIPTION:Moment generating functions (Laplace transforms) are a means for transforming probability problems into problems involving polynomials.  Here I will concentrate on the binomial distribution\, and use the mgf to link this distributions probabilities directly to the binomial theorem.  The mgf is also a key ingredient in Chernoff bounds\, which give upper bounds on the tail probabilities of binomial distributions (aka partial sums of the binomial theorem).  By employing the method of smoothing and tilting\, it is possible to attain bounds on the tails that go down faster than the traditional approximation heuristic that uses the Central Limit Theorem.
URL:https://colleges.claremont.edu/ccms/event/talk-by-mark-huber-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181030T121500
DTEND;TZID=America/Los_Angeles:20181030T131000
DTSTAMP:20260529T174915
CREATED:20180823T224159Z
LAST-MODIFIED:20181024T083012Z
UID:471-1540901700-1540905000@colleges.claremont.edu
SUMMARY:Uniform asymptotic growth of symbolic powers  (Robert Walker\, University of Michigan)
DESCRIPTION:Algebraic geometry (AG) is a major generalization of linear algebra which is fairly influential in mathematics. Since the 1980’s with the development of computer algebra systems like Mathematica\, AG has been leveraged in areas of STEM as diverse as statistics\, robotic kinematics\, computer science/geometric modeling\, and mirror symmetry. Part one of my talk will be a brief introduction to AG\, to two notions of taking powers of ideals (regular vs symbolic) in Noetherian commutative rings\, and to the ideal containment problem that I study in my thesis. Part two of my talk will focus on stating the main results of my thesis in a user-ready form\, giving a “comical” example or two of how to use them. At the risk of sounding like Paul Rudd in Ant-Man\, I hope this talk with be awesome.
URL:https://colleges.claremont.edu/ccms/event/tba-4/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181016T121500
DTEND;TZID=America/Los_Angeles:20181016T131000
DTSTAMP:20260529T174915
CREATED:20181008T194923Z
LAST-MODIFIED:20181008T194923Z
UID:897-1539692100-1539695400@colleges.claremont.edu
SUMMARY:The Bateman—Horn Conjecture\, Part I: heuristic derivation (Stephan Garcia\, Pomona)
DESCRIPTION:The Bateman—Horn Conjecture is a far-reaching statement about the distribution of the prime numbers.  It implies many known results\, such as the Green—Tao theorem\, and a variety of famous conjectures\, such as the Twin Prime Conjecture.  In this expository talk\, we start from basic principles and provide a heuristic argument in favor of the conjecture.  This talk should be accessible to undergraduates with a background in modular arithmetic.
URL:https://colleges.claremont.edu/ccms/event/the-bateman-horn-conjecture-part-i-heuristic-derivation-stephan-garcia-pomona/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181009T121500
DTEND;TZID=America/Los_Angeles:20181009T131000
DTSTAMP:20260529T174915
CREATED:20180912T160739Z
LAST-MODIFIED:20181001T220127Z
UID:546-1539087300-1539090600@colleges.claremont.edu
SUMMARY:State Polytopes of Combinatorial Neural Codes (Rob Davis\, HMC)
DESCRIPTION:Combinatorial neural codes are 0/1 vectors that are used to model the co-firing patterns of a set of place cells in the brain. One wide-open problem in this area is to determine when a given code can be algorithmically drawn in the plane as a Venn diagram-like figure. A sufficient condition to do so is for the code to have a property called k-inductively pierced. Gross\, Obatake\, and Youngs recently used toric algebra to show that a code on three neurons is 1-inductively pierced if and only if the toric ideal is trivial or generated by quadratics. No result is known for additional neurons in the same generality. \nIn this talk\, we study two infinite classes of combinatorial neural codes in detail. For each code\, we explicitly compute its universal Gröbner basis. This is done for the first class by recognizing that the codewords form a Lawrence-type matrix. With the second class\, this is done by showing that the matrix is totally unimodular. These computations allow one to compute the state polytopes of the corresponding toric ideals\, from which all distinct initial ideals may be computed efficiently. Moreover\, we show that the state polytopes are combinatorially equivalent to well-known polytopes: the permutohedron and the stellohedron.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-by-rob-davis-hmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20181002T121500
DTEND;TZID=America/Los_Angeles:20181002T131000
DTSTAMP:20260529T174915
CREATED:20180911T213738Z
LAST-MODIFIED:20180926T151643Z
UID:533-1538482500-1538485800@colleges.claremont.edu
SUMMARY:An Introduction to the Sato-Tate Conjecture (Edray Goins\, Pomona College)
DESCRIPTION:In 1846\, Ernst Eduard Kummer conjectured a distribution of values of a cubic Gauss sum after computing a few values by hand.  This was forgotten about for nearly 100 years until John von Neumann and Herman Goldstine attempted to verify the conjecture as a way to test the new ENIAC machine in 1953.  They found evidence that the conjecture was false\, but trusted Kummer more than they did their digital computer.  The conjecture would hold until 1979\, when Roger Heath-Brown and Samuel Patterson proved it to be false. \nA few years earlier in 1965\, Mikio Sato and John Tate independently came up with a conjecture which gave the correct distribution of these cubic Gauss sums — although it was expressed slightly differently in terms of counting points of elliptic curves over finite fields.  In this talk\, we give an overview of the Sato-Tate Conjecture\, present an approach by Jean-Pierre Serre following his paper from 1967\, then sketch the 2006 proof of the conjecture following the ideas of Laurent Clozel\, Michael Harris\, Nicholas Shepherd-Barron and Richard Taylor. \nHere are the slides of this lecture: Edray Goins’ slides.
URL:https://colleges.claremont.edu/ccms/event/talk-by-edray-goins-pomona-college/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20180925T121500
DTEND;TZID=America/Los_Angeles:20180925T131000
DTSTAMP:20260529T174915
CREATED:20180911T213219Z
LAST-MODIFIED:20180926T151534Z
UID:531-1537877700-1537881000@colleges.claremont.edu
SUMMARY:Quandle coloring quivers (Sam Nelson\, CMC)
DESCRIPTION:Given a finite quandle $X$\, a set $S \subset \mathrm{Hom}(X\,X)$ of quandle endomoprhisms\, and an oriented knot or link $L$\, we construct a quiver-valued invariant of oriented knots and links. This quiver categorifies the quandle counting invariant in the most literal sense and can be used to define many enhancements of the counting invariant. This is joint work with Harvey Mudd College student Karina Cho.
URL:https://colleges.claremont.edu/ccms/event/talk-by-sam-nelson-cmc/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20180918T121500
DTEND;TZID=America/Los_Angeles:20180918T131000
DTSTAMP:20260529T174915
CREATED:20180822T051451Z
LAST-MODIFIED:20180926T174121Z
UID:449-1537272900-1537276200@colleges.claremont.edu
SUMMARY:Inversions for reduced words (Sami Assaf\, USC)
DESCRIPTION:The number of inversions of a permutation is an important statistic that arises in many contexts\, including as the minimum number of simple transpositions needed to express the permutation and\, equivalently\, as the rank function for weak Bruhat order on the symmetric group. In this talk\, I’ll describe an analogous statistic on the reduced expressions for a given permutation that turns the Coxeter graph into a ranked poset with unique maximal element. This statistic simplifies greatly when shifting our paradigm from reduced expressions to balanced tableaux\, and I’ll use this simplification to give an elementary proof computing the diameter of the Coxeter graph for the long permutation. \nThis talk is elementary and assumes no background other than passing familiarity with the symmetric group.
URL:https://colleges.claremont.edu/ccms/event/tba-3/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20180911T121500
DTEND;TZID=America/Los_Angeles:20180911T131000
DTSTAMP:20260529T174915
CREATED:20180822T052223Z
LAST-MODIFIED:20180926T174358Z
UID:451-1536668100-1536671400@colleges.claremont.edu
SUMMARY:Small representations of integers by integral quadratic form (Lenny Fukshansky\, CMC)
DESCRIPTION:Given an isotropic integral quadratic form which assumes a value t\, we investigate the distribution of integer points at which this value is assumed. Building on the previous work about the distribution of small-height zeros of quadratic forms\, we produce bounds on height of points outside of some algebraic sets in a quadratic space at which the form assumes the value t. Our bounds on height are explicit in terms of heights of the form\, the space\, the algebraic set and the value t. Joint work with W. K. Chan. \nThe Fall 2018 organizational meeting for the ANTC seminar will be held at noon in the same room\, preceding the talk.
URL:https://colleges.claremont.edu/ccms/event/small-representations-of-integers-by-integral-quadratic-form/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR