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DTSTART;TZID=America/Los_Angeles:20241203T121500
DTEND;TZID=America/Los_Angeles:20241203T131000
DTSTAMP:20260418T072616
CREATED:20240906T182729Z
LAST-MODIFIED:20241118T192728Z
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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
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DTSTART;TZID=America/Los_Angeles:20241203T150000
DTEND;TZID=America/Los_Angeles:20241203T160000
DTSTAMP:20260418T072616
CREATED:20240928T045355Z
LAST-MODIFIED:20241202T162645Z
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SUMMARY:Claremont Topology Seminar: Rhea Palak Bakshi (University of California\, Santa Barbara)
DESCRIPTION:We welcome all undergraduate/graduate students and faculty to attend topology seminar! \nSpeaker: Rhea Palak Bakshi (University of California Santa Barbara) \nTitle: The skein module of the connected sum of two copies of L(0\,1) \nAbstract: Abstract: Skein modules were introduced by Jozef H. Przytycki\, and independently by Vladmimor Turaev\, as generalisations of the Jones\, Kauffman bracket\, and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) is the most extensively studied of all. However\, computing the KBSM of a 3-manifold is known to be notoriously hard\, especially over the ring of Laurent polynomials. Marche conjectured that over the ring of Laurent polynomials\, the KBSM of closed oriented 3-manifolds splits into the sum of free and torsion modules. The counterexample to this conjecture is given by the connected sum of two copies of the real projective space. With the goal of finding a definite structure of the KBSM over this ring\, we compute the skein module of S^1 x S^2 # H_1 and S^1 x S^2 # S^1 x S^2. We show that it is isomorphic to the KBSM of a genus two handlebody modulo some specific handle sliding relations. Moreover\, these handle sliding relations can be written in terms of Chebyshev polynomials. We also discuss whether the KBSM of these manifolds splits into the sums of free and torsion modules. This is joint work with Seongjeong Kim\, Shangjun Shi\, and Xiao Wang.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-rhea-palak-bakshi-university-of-california-santa-barbara/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
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DTSTART;TZID=America/Los_Angeles:20241204T153000
DTEND;TZID=America/Los_Angeles:20241204T173000
DTSTAMP:20260418T072616
CREATED:20241125T183109Z
LAST-MODIFIED:20241202T232529Z
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SUMMARY:CCMS Colloquium with Pre-Colloquium Reception:  Shahriar Shahriari (Pomona College)
DESCRIPTION:We will conclude the CCMS Fall Colloquium Series with a Pre-Colloquium Reception followed by a talk (details below). \nPre-Colloquium Reception will begin at 3:30pm with foods and drink in the Estella Atrium. \nFollowing the reception\, the colloquium talk will start at 4:30pm (Notice the change in time.) \n_____________________ \nSpeaker: Shahriar Shahriari\, Professor of Mathematics and Statistics\, Pomona College\, Claremont\, CA \nTitle:  Combinatorial Connections: HyperCubes & Vector Spaces Over Finite Fields \nAbstract: Abstractions allow us to see connections between familiar objects. In extremal set theory\, often the aim is to find the largest or smallest collection of subsets with a specific property. Using the lens of partially ordered sets\, one can investigate vector spaces over finite fields using vaguely similar techniques. If V is an n-dimensional vector space over a finite field\, then how many k-dimensional subspaces can you find so that your collection does not include three distinct subspaces A\, B\, and C with A = (A\cap B) \oplus (A \cap C)? How many subspaces of any dimension can you find so that your collection does not include three distinct subspaces A\, B\, and C with either $A  \subseteq B \cap C$ or $B+C \subseteq A$? These puzzles will illustrate the connections between combinatorics of finite sets and of vector spaces. \nBio:  Shahriari is the William Polk Russell Professor of Mathematics at Pomona College. He has had the privilege of teaching/mentoring generations of talented students\, many of whom are now teaching in universities and colleges across the country. \nIn 2015\, Shahriar Shahriari received a Mathematical Association of America Deborah and Franklin Tepper Haimo Award for Distinguished Teaching in Mathematics for his commitment to bringing more students from underrepresented groups into the field of mathematics — widely considered the nation’s top prize for teaching mathematics. He is a five-time winner of Pomona College’s Wig teaching award. Known for classes that encourage student-driven discovery\, he published the materials for his honors Calculus class as a textbook\, titled Approximately Calculus\, which won the American Library Association’s Choice Award for Outstanding Academic Title in 2007. Shahriari has published three texts: “Approximately Calculus”\, “Algebra in Action”\, and “An Invitation to Combinatorics”\, and over 50 articles\, many coauthored with undergraduate students.
URL:https://colleges.claremont.edu/ccms/event/shahriar-shahriari-ccms-fall-2024/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20241207T100000
DTEND;TZID=America/Los_Angeles:20241207T120000
DTSTAMP:20260418T072616
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SUMMARY:GEMS December 7th Session
DESCRIPTION:This GEMS session will be facilitated by Professor Lenny Fukshansky from Claremont McKenna College. \nTitle:  From Knapsacks and Changing Coins to Geometry\n\nAbstract:  Suppose you have a bag that can hold a fixed amount of weight\, and you are trying to fill it with several types of objects of different weights and prices. The goal is to maximize the value of your bag. How do you do it? This is a notoriously difficult optimization problem\, which often arises in resource allocation with financial constraints. Another famous optimization problem asks what amount of change can you give with coins of prescribed denominations? Surprisingly\, not only are the two closely related to each other\, they both can be restated in the geometric language of polygons\, points with integer coordinates\, and their higher-dimensional generalizations! We will discuss these important problems and their beautiful connection to a classical problem in geometry: how can we count the number of integer points in a fixed polygon? The answer is given by the celebrated 19th century theorem of Georg Alexander Pick\, who proved a remarkable formula for this number in terms of the area and perimeter of the polygon. We will talk about Pick’s theorem and perform a hands-on exploration of this fascinating area of geometry.
URL:https://colleges.claremont.edu/ccms/event/gems-december-7th-session/
LOCATION:Shanahan 1480\, Harvey Mudd College\, 301 Platt Blvd.\, Claremont\, CA\, 91711\, United States
CATEGORIES:GEMS
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