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DTSTART;TZID=America/Los_Angeles:20240416T121500
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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
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DTSTART;TZID=America/Los_Angeles:20240416T150000
DTEND;TZID=America/Los_Angeles:20240416T160000
DTSTAMP:20260413T145142
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LAST-MODIFIED:20240414T212101Z
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SUMMARY:Claremont Topology Seminar: Ryan Maguire (Dartmouth College)
DESCRIPTION:We especially welcome all undergraduates and graduate students to attend topology seminar! \nSpeaker: Ryan Maguire (Dartmouth College) \nTitle: Relative Strengths of Knot Invariants by Experiment \nAbstract: Four knot polynomials have been well studied by topologists\, graph theorists\, and algebraists alike:\nThe Alexander\, Jones\, HOMFLY-PT\, and Khovanov polynomials. It is known that the Khovanov polynomial is “stronger” than the Jones polynomial\, and similarly one may state that HOMFLY-PT is stronger than both the Alexander and Jones polynomials. No comparison can be made between the Jones and Alexander polynomials since there are families of knots with identical Alexander polynomials but distinct Jones polynomials\, and vice-versa\, but experiment tells us the Jones polynomial is stronger\, on average\, at distinguishing knots. We have tabulated the Alexander\, Jones\, and HOMFLY-PT polynomials for all knots up to 19 crossings\, and the Khovanov polynomial for up to 17 crossings. Using this\, we can experiment on the relative strengths of these knot invariants and generate statistics on them.
URL:https://colleges.claremont.edu/ccms/event/claremont-topology-seminar-ryan-maguire-dartmouth-college/
LOCATION:Estella 2099
CATEGORIES:Topology Seminar
ORGANIZER;CN="Bahar Acu":MAILTO:Bahar_Acu@pitzer.edu
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DTSTART;TZID=America/Los_Angeles:20240417T161500
DTEND;TZID=America/Los_Angeles:20240417T173000
DTSTAMP:20260413T145142
CREATED:20240412T211923Z
LAST-MODIFIED:20240412T211923Z
UID:3436-1713370500-1713375000@colleges.claremont.edu
SUMMARY:Structural Ramsey Theory and Logic (Lynn Scow\, CSUSB)
DESCRIPTION:Title: Structural Ramsey Theory and Logic \nSpeaker: Lynn Scow\, Professor of Mathematics\, California State University\, San Bernardino \nAbstract: The connection between Ramsey theory and logic goes back to Frank P. Ramsey’s 1929 paper in which he announced his famous Ramsey theorem for finite sequences.  This theorem states that for any partition of all sequences of length $k$ from $\mathbb{N}$ into finitely many pieces\, there is an infinite subset $X \subset \mathbb{N}$ such that all sequences of length $k$ from $X$ lie in one piece of this partition.  In the intervening years\, Ramsey theory has been used to study problems in logic\, and vice versa.  In this talk\, I will survey some results from the last few decades\, as well as highlight some results obtained with my coauthor Dana Bartošová at University of Florida. \n\n\n\n\n\nLynn Scow studied mathematics and philosophy at UC Berkeley as an undergraduate and continued on to earn her Ph.D. in mathematics from UC Berkeley.  She then held a postdoctoral position at University of Illinois Chicago followed by a visiting position at Vassar College\, and is currently faculty at California State University\, San Bernardino.  Her research area is primarily in foundations and mathematical logic\, including applications of structural Ramsey theory to model theory and vice versa.  She treasures mathematics for the conversations\, the shared understandings\, and the joy.
URL:https://colleges.claremont.edu/ccms/event/structural-ramsey-theory-and-logic-lynn-scow-csusb/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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