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DTSTART;TZID=America/Los_Angeles:20250401T121500
DTEND;TZID=America/Los_Angeles:20250401T131000
DTSTAMP:20260425T041210
CREATED:20250206T191602Z
LAST-MODIFIED:20250326T164610Z
UID:3688-1743509700-1743513000@colleges.claremont.edu
SUMMARY:Permutation pattern avoidance\, alternating sign matrices\, and asymptotics (Justin Troyka\, Cal State LA)
DESCRIPTION:A big area in combinatorics over the last several decades has been the study of pattern-avoiding permutations\, whose enumeration is exciting and mysterious. Alternating sign matrices (ASMs) are a generalization of permutations whose study in combinatorics has also been exciting and mysterious. In this talk\, I will explain some new asymptotic results involving the number of ASMs that avoid a given permutation pattern\, from my joint work with Mathilde Bouvel\, Eric Egge\, Rebecca Smith\, and Jessica Striker. I will also show some of the highlights in the histories of both pattern-avoiding permutations and ASMs.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-justin-troyka-cal-state-la/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250325T121500
DTEND;TZID=America/Los_Angeles:20250325T131000
DTSTAMP:20260425T041210
CREATED:20250127T201036Z
LAST-MODIFIED:20250324T151237Z
UID:3659-1742904900-1742908200@colleges.claremont.edu
SUMMARY:Some Diophantine analogies between Dirichlet series and polynomials (Vesselin Dimitrov\, Caltech)
DESCRIPTION:I will present an integral — requiring no character twists — converse theorem for recognizing when is a Dirichlet series with algebraic integer coefficients equal to the L-function of a modular form. This refines the unbounded denominators conjecture of Atkin and Swinnerton-Dyer. Analogies with basic function field arithmetic then suggest a quantitative refinement which precludes a pair of GL(2) automorphic L-functions with closely matched up zeros. I will explain how to get at such a theorem. 
URL:https://colleges.claremont.edu/ccms/event/antc-talk-vesselin-dimitrov-caltech/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250302T121500
DTEND;TZID=America/Los_Angeles:20250304T131000
DTSTAMP:20260425T041210
CREATED:20250302T201628Z
LAST-MODIFIED:20250302T201628Z
UID:3716-1740917700-1741093800@colleges.claremont.edu
SUMMARY:Enumerative Invariants from Derived Categories III (Reginald Anderson\, CMC)
DESCRIPTION:We’ll first define the two-point gravitational correlators which appeared last week as descendant Gromov-Witten invariants. By request\, we’ll then introduce Gromov-Witten invariants as they appear in the expository work https://arxiv.org/abs/2501.03232 and give CP^1 to demonstrate some of the identities which GW invariants satisfy. If time allows\, we’ll also give the small and big quantum cohomology for CP^1.
URL:https://colleges.claremont.edu/ccms/event/enumerative-invariants-from-derived-categories-iii-reginald-anderson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250225T121500
DTEND;TZID=America/Los_Angeles:20250225T131000
DTSTAMP:20260425T041210
CREATED:20250218T192927Z
LAST-MODIFIED:20250218T193027Z
UID:3709-1740485700-1740489000@colleges.claremont.edu
SUMMARY:Enumerative invariants from derived categories -- part II (Reginald Anderson\, CMC)
DESCRIPTION:Following Kalashnikov\, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
URL:https://colleges.claremont.edu/ccms/event/enumerative-invariants-from-derived-categories-part-ii-reginald-anderson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250218T121500
DTEND;TZID=America/Los_Angeles:20250218T131000
DTSTAMP:20260425T041210
CREATED:20250212T225636Z
LAST-MODIFIED:20250218T192952Z
UID:3696-1739880900-1739884200@colleges.claremont.edu
SUMMARY:Enumerative invariants from derived categories -- part I (Reginald Anderson\, CMC)
DESCRIPTION:Following Kalashnikov\, we recover Givental’s small J function for CP^1 by viewing it as a quiver flag variety.
URL:https://colleges.claremont.edu/ccms/event/enumerative-invariants-from-derived-categories-reginald-anderson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250211T121500
DTEND;TZID=America/Los_Angeles:20250211T131000
DTSTAMP:20260425T041210
CREATED:20250206T203702Z
LAST-MODIFIED:20250206T203729Z
UID:3689-1739276100-1739279400@colleges.claremont.edu
SUMMARY:On the illumination problem for convex sets (Lenny Fukshansky\, CMC)
DESCRIPTION:Let K be a compact convex set in the Euclidean space R^n. How many lights are needed to illuminate its boundary? A classical conjecture of Boltyanskii (1960) asserts that 2^n lights are sufficient to illuminate any such set K. While this is still open\, an earlier observation of Hadwiger (1945) guarantees that if K has smooth boundary\, then n+1 lights are sufficient: we only need to position these lights at the vertices of a simplex containing K in its interior. In fact\, this observation allows us to estimate how far from K these lights need to be. A more delicate problem arises if we insist on placing the lights at points of a fixed lattice L: how far from K must the lights be then? We discuss this problem\, producing a bound on this distance\, which depends on certain orthogonality and symmetry properties of the lattice in question. Interestingly\, for some nice classes of lattices\, a bound independent of L can be produced.
URL:https://colleges.claremont.edu/ccms/event/on-the-illumination-problem-for-convex-sets/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20250204T121500
DTEND;TZID=America/Los_Angeles:20250204T131000
DTSTAMP:20260425T041210
CREATED:20250123T065341Z
LAST-MODIFIED:20250123T065341Z
UID:3639-1738671300-1738674600@colleges.claremont.edu
SUMMARY:Quandle cohomology quiver representations (Sam Nelson\, CMC)
DESCRIPTION:Quandles are algebraic structures encoding the motion of knots through space. Quandle cocycle quivers categorify the quandle cocycle invariant. In this talk we will define a quiver representation associated to quandle cocycle quivers and use it to obtain new polynomial invariants of knots.
URL:https://colleges.claremont.edu/ccms/event/quandle-cohomology-quiver-representations-sam-nelson-cmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241203T121500
DTEND;TZID=America/Los_Angeles:20241203T131000
DTSTAMP:20260425T041210
CREATED:20240906T182729Z
LAST-MODIFIED:20241118T192728Z
UID:3497-1733228100-1733231400@colleges.claremont.edu
SUMMARY:Variations of oddtown and eventown (Jason O'Neill\, Cal State LA)
DESCRIPTION:The classical oddtown and eventown problems involve a collection of subsets of a finite set with an odd (resp. even) number of elements such that all pairwise intersections contain an even number of elements. In this talk\, we will discuss these results as well as the following variants: \n\nWe consider set sizes and pairwise intersection restrictions given modulo m as opposed to even/odd (mod 2).\nWe allow very “few” pairwise intersections in collections of subsets.\nWe impose further conditions on 3-wise and 4-wise intersections of our collection of subsets.\n\nAlong the way\, we will sprinkle in a few open problems.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-jason-oneill-cal-state-la/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241112T121500
DTEND;TZID=America/Los_Angeles:20241112T131000
DTSTAMP:20260425T041210
CREATED:20240118T205450Z
LAST-MODIFIED:20241028T192316Z
UID:3341-1731413700-1731417000@colleges.claremont.edu
SUMMARY:Traces of Partition Eisenstein series (Ken Ono\, University of Virginia)
DESCRIPTION:Integer partitions are ubiquitous in mathematics\, arising in subjects as disparate as algebraic combinatorics\, algebraic geometry\, number theory\, representation theory\, to mathematics physics. Many of the deepest results on partitions have their origin in the work of Ramanujan. In this lecture\, we will describe a completely new and unexpected role for partitions that also arises from the mysterious “lost notebook” of Ramanujan. We discover and explain the role of new q-series called “partition Eisenstein series”. These functions magically pop up as the key device for solving a conjecture of Andrews and Berndt\, for studying symmetric functions of 2-dimensional lattice sums\, for determining the properties of Andrews-Garvan “crank statistic”\, and for representing the Taylor coefficients of virtually every interesting Jacobi automorphic form. This talk will tell the story of the recent discovery of these functions\, and will offer a brief tour of these applications.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-ken-ono-university-of-virginia/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241105T121500
DTEND;TZID=America/Los_Angeles:20241105T131000
DTSTAMP:20260425T041210
CREATED:20240912T211317Z
LAST-MODIFIED:20241025T000409Z
UID:3512-1730808900-1730812200@colleges.claremont.edu
SUMMARY:Noether-Lefschetz theory and class groups (John Brevik\, Cal State Long Beach)
DESCRIPTION:The classical Noether-Lefschetz Theorem states that a suitably general algebraic surface S of degree d ≥ 4 in complex projective 3-space P3 contains no curves besides complete intersections\, that is\, curves of the form S ∩ T where T is another surface. After discussing briefly Noether’s non-proof of this theorem and hinting at the idea behind Lefschetz’s proof\, I will sketch some of our recent progress in generalizing this theorem and its implications for global and local divisor class groups. We explore the question of what class groups are possible for local rings on surfaces in a particular analytic isomorphism class and show the ubiquitousness of unique factorization domains among such rings. Joint work with Scott Nollet (Texas Christian University).
URL:https://colleges.claremont.edu/ccms/event/antc-talk-john-brevik-cal-state-long-beach/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241029T121500
DTEND;TZID=America/Los_Angeles:20241029T131000
DTSTAMP:20260425T041210
CREATED:20240903T234219Z
LAST-MODIFIED:20241023T053311Z
UID:3487-1730204100-1730207400@colleges.claremont.edu
SUMMARY:Sequences with identical autocorrelation spectra (Daniel Katz\, Cal State Northridge)
DESCRIPTION:In this talk\, we explore sequences and their autocorrelation functions. Knowing the autocorrelation function of a sequence is equivalent to knowing the magnitude of its Fourier transform.  Resolving the lack of phase information is called the phase problem.  We say that two sequences are equicorrelational to mean that they have the same aperiodic autocorrelation function.  We investigate the necessary and sufficient conditions for two sequences to be equicorrelational\, where\nwe take into consideration the alphabet from which their terms are drawn.  There are trivial forms of equicorrelationality arising from modifications that predictably preserve the autocorrelation\, for example\, negating the sequence or writing the sequence in reverse order and then complex conjugating every term.  By an exhaustive search of binary sequences up to length $44$\, we find that nontrivial equicorrelationality among binary sequences does occur\, but is rare.  We say that a positive integer $n$ is {\it unequivocal} to mean that there is no pair of nontrivially equicorrelational binary sequences of length $n$; otherwise $n$ is {\it equivocal}.  For integers $n \leq 44$\, we found that the unequivocal ones are $1$–$8$\, $10$\, $11$\, $13$\, $14$\, $19$\, $22$\, $23$\, $26$\, $29$\, $37$\, and $38$.  We prove that any multiple of a equivocal number is also equivocal\, and pose open questions as to whether there are finitely or infinitely many unequivocal numbers and whether the probability of nontrivial equicorrelationality occurring tends to zero as the sequence length tends to infinity.  (This is joint work with Adeebur Rahman and Michael J Ward.)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-cal-state-northridge-2/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241022T121500
DTEND;TZID=America/Los_Angeles:20241022T131000
DTSTAMP:20260425T041210
CREATED:20240909T190346Z
LAST-MODIFIED:20241016T201124Z
UID:3502-1729599300-1729602600@colleges.claremont.edu
SUMMARY:Making sandwiches: a novel invariant in D-module theory (David Lieberman\, HMC)
DESCRIPTION:In the field of commutative algebra\, the principal object of study is (unsurprisingly) commutative algebras. A somewhat unintuitive fact is that results about commutative algebras can be gleaned from an associated non-commutative algebra whose generators are very analytic in nature. This object is called the ring of differential operators\, often denoted by D. In a sense gives an algebraic way of constructing the partial derivative.\n\nAn important result in the study of D-modules is Bernstein’s inequality\, first proved by Joseph Bernstein in the 1970’s. The result gives a lower bound on the filtered dimension of a D-module\, which a provide insights about modules of commutative algebras. The goal of this talk is to present some novel singular settings where this inequality holds. To do this\, we will introduce an invariant called sandwich Bernstein-Sato polynomials. These are analogous to a well studied object called the Bernstein-Sato polynomial\, which is a generalization of the power rule taught in undergraduate calculus courses. Using sandwich Bernstein-Sato polynomials\, we will show that Bernstein’s inequality holds true for the differential operators of the coordinate ring of the Segre product of projective spaces.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-david-lieberman-hmc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241008T121500
DTEND;TZID=America/Los_Angeles:20241008T131000
DTSTAMP:20260425T041210
CREATED:20240901T163937Z
LAST-MODIFIED:20240929T202957Z
UID:3482-1728389700-1728393000@colleges.claremont.edu
SUMMARY:Counting matrix points via lattice zeta functions (Yifeng Huang\, USC)
DESCRIPTION:​I will introduce two general problems and explain how they surprisingly connect with each other and with other aspects of mathematics (for a glimpse\, Sato—Tate\, hypergeometric functions\, moduli spaces of sheaves\, Catalan numbers\, Hall polynomials\, etc.)​.\n\nThe first problem is to count finite-field points on so called “varieties of matrix points”. They are created from a simple and fully elementary recipe and can yet easily get very complicated. The second problem is analogous to counting full-rank sublattices of $\mathbb{Z}^d$ with index $n$\, but with $\mathbb{Z}$ replaced by non-Dedekind rings\, such as non-maximal orders in number fields. (Containing joint work with Ken Ono\, Hasan Saad and joint work with Ruofan Jiang)
URL:https://colleges.claremont.edu/ccms/event/antc-talk-yifeng-huang-usc/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241001T121500
DTEND;TZID=America/Los_Angeles:20241001T131000
DTSTAMP:20260425T041210
CREATED:20240827T194511Z
LAST-MODIFIED:20241001T153641Z
UID:3473-1727784900-1727788200@colleges.claremont.edu
SUMMARY:Adinkras as Origami? (Edray Goins\, Pomona College)
DESCRIPTION:Around 20 years ago\, physicists Michael Faux and Jim Gates invented Adinkras as a way to better understand Supersymmetry.  These are bipartite graphs whose vertices represent bosons and fermions and whose edges represent operators which relate the particles.  Recently\, Charles Doran\, Kevin Iga\, Jordan Kostiuk\, Greg Landweber and Stefan M\'{e}ndez-Diez determined that Adinkras are a type of Dessin d’Enfant; they showed this by explicitly exhibiting a Belyi map as a composition $\beta: S \to \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C)$.  They computed the first arrow as a map from a certain compact connected Riemann surface $S$ to the Riemann sphere $\mathbb P^1(\mathbb C) \simeq S^2(\mathbb R)$\, and the second as a map which keeps track of the “coloring” of the edges.\n\nAdinkras naturally have square faces.  This keeps track of the non-commutative nature of the supersymmetric operators.  While Dessin d’Enfants correspond to triangular tilings of Riemann surfaces\, there is a similar construction — called “origami” — which correspond to square tilings.  In this project\, we attempt to discover how to express the construction of Doran\, et al. as a composition $\beta: S \to E(\mathbb C) \to \mathbb P^1(\mathbb C)$ for some elliptic curve elliptic curve $E$ such that the map corresponds to an “origami”\, that is\, a map which is branched over just one point.  This work is conducted as part of the Pomona Research in Mathematics Experience (DMS-2113782).
URL:https://colleges.claremont.edu/ccms/event/adinkras-as-origami-edray-goins-pomona-college/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240924T121500
DTEND;TZID=America/Los_Angeles:20240924T131000
DTSTAMP:20260425T041210
CREATED:20240825T022324Z
LAST-MODIFIED:20240825T022447Z
UID:3467-1727180100-1727183400@colleges.claremont.edu
SUMMARY:Presentations of derived categories (Reginald Anderson\, CMC)
DESCRIPTION:A modification of the cellular resolution of the diagonal given by Bayer-Popescu-Sturmfels gives a virtual resolution of the diagonal for smooth projective toric varieties and toric Deligne-Mumford stacks which are a global quotient of a smooth projective variety by a finite abelian group. In the past year\, Hanlon-Hicks-Lazarev gave a minimal resolution of the diagonal for toric subvarieties of smooth projective toric varieties. We give implications for exceptional collections on smooth projective toric Fano varieties in dimensions 1-4. This is joint work with CMC undergrads Justin Son\, Hill Zhang\, and Jumari Querimit-Ramirez.
URL:https://colleges.claremont.edu/ccms/event/localization-techniques-in-equivariant-cohomology-reginald-anderson-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240917T121500
DTEND;TZID=America/Los_Angeles:20240917T131000
DTSTAMP:20260425T041210
CREATED:20240824T183435Z
LAST-MODIFIED:20240906T183313Z
UID:3464-1726575300-1726578600@colleges.claremont.edu
SUMMARY:Biquandle module quiver representations (Sam Nelson\, CMC)
DESCRIPTION:Biquandle module enhancements are invariants of knots and links generalizing the classical Alexander module invariant. A quiver categorification of these invariants was introduced in 2020. In this work-in-progress (joint with Yewon Joung from Hanyang University in Seoul) we take the next step by defining invariant quiver representations. As an application we obtain new polynomial knot invariants as decategorifications.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-sam-nelson-cmc-4/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240910T121500
DTEND;TZID=America/Los_Angeles:20240910T131000
DTSTAMP:20260425T041210
CREATED:20240825T022632Z
LAST-MODIFIED:20240906T182843Z
UID:3469-1725970500-1725973800@colleges.claremont.edu
SUMMARY:Localization techniques in equivariant cohomology (Reginald Anderson\, CMC)
DESCRIPTION:In order to understand a topological space X\, it is often easier to understand X in terms of an action by a group G. When X is a compact complex manifold\, we often let G be products of S^1 or \C^* acting in a nice way (“holomorphically”) on X. This simplifies several calculations of an Euler characteristic by considering the torus-fixed loci; examples are given throughout.\n\nThe notes for this talk can be found here:\n\nhttps://drive.google.com/file/d/1FjhKDeJLIPQBlLA-x-BsnkosNayZMSAn/view?usp=sharing
URL:https://colleges.claremont.edu/ccms/event/localization-techniques-in-equivariant-cohomology-reginald-anderson-cmc-2/
LOCATION:Estella 2113
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240903T121500
DTEND;TZID=America/Los_Angeles:20240903T131000
DTSTAMP:20260425T041210
CREATED:20240824T184428Z
LAST-MODIFIED:20240824T184428Z
UID:3465-1725365700-1725369000@colleges.claremont.edu
SUMMARY:Lattice angles and quadratic forms (Lenny Fukshansky\, CMC)
DESCRIPTION:What are the possible angles between two integer vectors in R^n? If we fix one such possible angle and one integer vector x\, is there always another integer vector y that makes this angle with x? Assuming that x makes a given angle with some vector\, how can we find the shortest such vector y? What if we designate a forbidden set of vectors\, what is the shortest y making a given angle with x outside of this forbidden set? It turns out that all of these questions can be reformulated in terms of a search for zeros of integral quadratic forms\, a rich arithmetic theory. We will give an introduction to this research direction and also show some of our recent results. Joint work with Sehun Jeong (CGU).
URL:https://colleges.claremont.edu/ccms/event/lattice-angles-and-quadratic-forms-lenny-fukshansky-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240430T121500
DTEND;TZID=America/Los_Angeles:20240430T131000
DTSTAMP:20260425T041210
CREATED:20240212T222657Z
LAST-MODIFIED:20240424T225203Z
UID:3383-1714479300-1714482600@colleges.claremont.edu
SUMMARY:Negligible cohomology (Matthew Gherman\, Caltech)
DESCRIPTION:For a finite group G\, a G-module M\, and a field F\, an element u in H^d(G\,M) is negligible over F if for each field extension L/F and every continuous group homomorphism from Gal(L^{sep}/L) to G\, u is in the kernel of the induced homomorphism H^d(G\,M) to H^d(L\,M). Negligible cohomology was first introduced by Serre and has deep connections with the embedding problem\, cohomological invariants\, and the profinite inverse Galois problem. Professor Alexander Merkurjev (UCLA) and I were able to compute negligible cohomology in degree 2\, compute the mod p negligible cohomology of elementary abelian p-groups\, and determine the Krull dimension of the quotient of mod p cohomology by the ideal of negligible elements.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-matthew-gherman-cal-tech/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240423T121500
DTEND;TZID=America/Los_Angeles:20240423T131000
DTSTAMP:20260425T041210
CREATED:20240326T205445Z
LAST-MODIFIED:20240326T205445Z
UID:3419-1713874500-1713877800@colleges.claremont.edu
SUMMARY:Clocks\, parking garages\, and the solvability of the quintic: a friendly introduction to monodromy (Edray Goins\, Pomona College)
DESCRIPTION:Imagine the hands on a clock.  For every complete the minute hand makes\, the seconds hand makes 60\, while the hour hand only goes one twelfth of the way.   We may think of the hour hand as generating a group such that when we “move” twelve times then we get back to where we started.  This is the elementary concept of a monodromy group. In this talk\, we give a gentle introduction to a historical mathematical concept which relates calculus\, linear algebra\, differential equations\, and group theory into one neat theory called “monodromy”.  We explore lots of real world applications\, including why it’s so easy to get lost in parking garages\, and present some open problems in the field.  We end the talk with a discussion of how this is all related to solving polynomial equations\, such as Abel’s famous theorem on the insolubility of the quintic by radicals.
URL:https://colleges.claremont.edu/ccms/event/clocks-parking-garages-and-the-solvability-of-the-quintic-a-friendly-introduction-to-monodromy-edray-goins-pomona-college/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240416T121500
DTEND;TZID=America/Los_Angeles:20240416T131000
DTSTAMP:20260425T041210
CREATED:20240324T220030Z
LAST-MODIFIED:20240326T015954Z
UID:3416-1713269700-1713273000@colleges.claremont.edu
SUMMARY:Primitive elements in number fields and Diophantine avoidance (Lenny Fukshansky\, CMC)
DESCRIPTION:The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K\, called a primitive element. In fact\, it is clear from the proof of this theorem that not only there are infinitely many such primitive elements in K\, but in fact most elements in K are primitive. This observation raises the question about finding a primitive element of small “size”\, where the standard way of measuring size is with the use of a height function. We discuss some conjectures and known results in this direction\, as well as some of our recent work on a variation of this problem which includes some additional avoidance conditions. Joint work with Sehun Jeong (CGU).
URL:https://colleges.claremont.edu/ccms/event/primitive-elements-in-number-fields-and-diophantine-avoidance-lenny-fukshansky-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240409T121500
DTEND;TZID=America/Los_Angeles:20240409T131000
DTSTAMP:20260425T041210
CREATED:20240328T182316Z
LAST-MODIFIED:20240330T202911Z
UID:3421-1712664900-1712668200@colleges.claremont.edu
SUMMARY:Building TOWARD Geometry: Truncated Octahedra work as Rhombic Dodecahedra (Peter Kagey\, HMC)
DESCRIPTION:In late March\, students\, staff\, and faculty were invited to help collaboratively build a large-scale geometric sculpture on the campus of Harvey Mudd College\, demonstrating a relationship between truncated octahedra and rhombic dodecahedra\, which are two examples of space-filling polyhedra. I’ll talk about the process of designing and building the sculpture\, some geometry and combinatorics underlying the construction\, and some discoveries we made along the way.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-peter-kagey-hmc-2/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240402T121500
DTEND;TZID=America/Los_Angeles:20240402T131000
DTSTAMP:20260425T041210
CREATED:20231024T210058Z
LAST-MODIFIED:20240326T205224Z
UID:3301-1712060100-1712063400@colleges.claremont.edu
SUMMARY:Well-rounded lattices and security: what we (don't) know (Camilla Hollanti\, Aalto University\, Finland)
DESCRIPTION:I will give a brief introduction to well-rounded lattices and to their utility in wireless communications and post-quantum security. We will see how the lattice theta series naturally arises in these contexts and discuss its connections to well-rounded lattices. The talk is based on joint work with Laia Amoros\, Amaro Barreal\, Taoufiq Damir\, Oliver Gnilke\, David Karpuk\, Alex Karrila\, Niklas Miller\, and Ha Tran.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-camilla-hollanti-aalto-university-finland/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240326T121500
DTEND;TZID=America/Los_Angeles:20240326T131000
DTSTAMP:20260425T041210
CREATED:20231215T050545Z
LAST-MODIFIED:20240312T172417Z
UID:3331-1711455300-1711458600@colleges.claremont.edu
SUMMARY:Sublattices and subrings of Z^n and random finite abelian groups (Nathan Kaplan\, UC Irvine)
DESCRIPTION:How many sublattices of Zn have index at most X?  If we choose such a lattice L at random\, what is the probability that Zn/L is cyclic?  What is the probability that its order is odd?  Now let R be a random subring of Zn.  What is the probability that Zn/R is cyclic?  We will see how these questions fit into the study of random groups in number theory and combinatorics.  We will discuss connections to Cohen-Lenstra heuristics for class groups of number fields\, sandpile groups of random graphs\, and cokernels of random matrices over the integers.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-nathan-kaplan-uc-irvine/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240319T121500
DTEND;TZID=America/Los_Angeles:20240319T131000
DTSTAMP:20260425T041210
CREATED:20231025T032921Z
LAST-MODIFIED:20240206T000905Z
UID:3302-1710850500-1710853800@colleges.claremont.edu
SUMMARY:Almost-prime times in horospherical flows (Taylor McAdam\, Pomona)
DESCRIPTION:There is a rich connection between homogeneous dynamics and number theory.  Often in such applications it is desirable for dynamical results to be effective (i.e. the rates of convergence for dynamical phenomena are known).  In the first part of this talk\, I will provide the necessary background and relevant history to state an effective equidistribution result for horospherical flows on the space of unimodular lattices in R^n.  I will then describe an application to studying the distribution of almost-prime times (integer times having fewer than a fixed number of prime factors) in horospherical orbits and discuss connections of this work to Sarnak’s Mobius disjointness conjecture.  In the second part of the talk I will describe some of the ingredients and key steps that go into proving these results. If time allows\, I will conclude by discussing recent results and ongoing work with M. Luethi that strengthens and generalizes this work.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-taylor-mcadam-pomona/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240305T121500
DTEND;TZID=America/Los_Angeles:20240305T131000
DTSTAMP:20260425T041210
CREATED:20240206T040319Z
LAST-MODIFIED:20240206T040319Z
UID:3376-1709640900-1709644200@colleges.claremont.edu
SUMMARY:Homological mirror symmetry\, curve counting\, and a classical example: 27 lines on a nonsingular cubic surface (Reggie Anderson\, CMC)
DESCRIPTION:Though mirror symmetry requires much technical background\, it gained traction in the mathematical community when physicists Candelas-de la Ossa-Green-Parkes discovered enumerative invariants counting the number of rational degree d curves inside of certain space called a “quintic threefold.” This answered longstanding problems in enumerative geometry from antiquity. In particular\, the number of rational degree d=1 curves inside of the space counts the number of lines. We will review a simpler\, classical example: any nonsingular cubic surface contains exactly 27 lines.
URL:https://colleges.claremont.edu/ccms/event/homological-mirror-symmetry-curve-counting-and-a-classical-example-27-lines-on-a-nonsingular-cubic-surface-reggie-anderson-cmc/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240227T121500
DTEND;TZID=America/Los_Angeles:20240227T131000
DTSTAMP:20260425T041210
CREATED:20240126T230120Z
LAST-MODIFIED:20240221T014138Z
UID:3354-1709036100-1709039400@colleges.claremont.edu
SUMMARY:The restricted variable Kakeya problem (Pete Clark\, University of Georgia)
DESCRIPTION:For a finite field F_q\, a subset of F_q^N is a Kakeya set if it contains a line in every direction (i.e.\, a coset of every one-dimensional linear subspace).  The finite field Kakeya problem is to determine the minimal size K(N\,q) of a Kakeya set in F_q^N.  This problem was posed by Wolff in 1999 as an analogue to the Kakeya problem in Euclidean N-space\, which was (and still is) one of the major open problems in harmonic analysis.  It caused quite a stir in 2008 when Zeev Dvir showed that for each fixed N\, as q -> oo\, K(N\,q) is bounded below by a constant times q^N: the Euclidean analogue of this result is not only proved but known to be false.\n\nBut what about the constant?  In 2009 Dvir-Kopparty-Saraf-Sudan gave a lower bound on K(N\,q) that was within a factor of 2 of an upper bound due to Dvir-Thas.  (I will briefly mention recent work of Bukh-Chao giving a decisive further improvement\, but that is not the focus of the talk.) The key to this improved lower bound is a multiplicity enhancement of a 1922 result of Ore. In this talk I want to give my own exposition of this work together with a mild generalization: if X is a subset of F_q^N \ {0}\, then an X-Kakeya set is a subset that contains a translate of the line generated by x for all x in X.  Putting K_X(N\,q) to be the minimal size of an X-Kakeya set in F_q^N\, I will give a lower bound on K_X(N\,q) that recovers the DKSS bound when X = F_q^N \ {0}.  This is similar in spirit to  “statistical Kakeya” results of Dvir and DKSS but not overlapping much; in fact\, I will give a statistical generalization of my result as well.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-pete-clark-university-of-georgia/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240220T121500
DTEND;TZID=America/Los_Angeles:20240220T131000
DTSTAMP:20260425T041210
CREATED:20231127T045722Z
LAST-MODIFIED:20240219T164238Z
UID:3328-1708431300-1708434600@colleges.claremont.edu
SUMMARY:Point-counting and topology of algebraic varieties (Siddarth Kannan\, UCLA)
DESCRIPTION:A projective algebraic variety X is the zero locus of a collection of homogeneous polynomials\, in projective space. When the polynomials have integer coefficients\, we can think of the k-valued points X(k) of the variety\, for any field k. Now suppose we have two different fields k and k’. How does the behavior of X(k) inform the behavior of X(k’)? It turns out that this is a rich line of inquiry. I will present a particularly pleasing example which relates the topology of the complex-valued points of X with the number of points it has over finite fields.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-siddarth-kannan-ucla/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240213T121500
DTEND;TZID=America/Los_Angeles:20240213T131000
DTSTAMP:20260425T041210
CREATED:20240116T192503Z
LAST-MODIFIED:20240116T202510Z
UID:3335-1707826500-1707829800@colleges.claremont.edu
SUMMARY:Quiver categorification of quandle invariants (Sam Nelson\, CMC)
DESCRIPTION:Quiver structures are naturally associated to subsets of the endomorphism sets of quandles and other knot-coloring structures\, providing a natural form of categorification of homset invariants and their enhancements. In this talk we will survey recent work in this area.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-sam-nelson-cmc-3/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240123T121500
DTEND;TZID=America/Los_Angeles:20240123T131000
DTSTAMP:20260425T041210
CREATED:20231020T203433Z
LAST-MODIFIED:20240117T005624Z
UID:3294-1706012100-1706015400@colleges.claremont.edu
SUMMARY:Using quantum statistical mechanical systems to study real quadratic fields (Jane Panangaden\, Pitzer College)
DESCRIPTION:The original Bost-Connes system was constructed in 1990 and is a QSM system with deep connections to the field of rationals. In particular\, its partition function is the Riemann-zeta function and its ground states evaluated on certain arithmetic objects yield generators of the maximal Abelian extension of the rationals. In this talk we describe the construction of a related QSM system adapted to the study of real quadratic fields\, called the Boundary GL2 System. We describe its thermal properties and show how these relate to class field theory of real quadratic fields. These results are joint work with Matilde Marcolli.
URL:https://colleges.claremont.edu/ccms/event/antc-seminar-jane-panangaden-pitzer-college/
LOCATION:Estella 2099
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR