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DTSTART;TZID=America/Los_Angeles:20231101T161500
DTEND;TZID=America/Los_Angeles:20231101T173000
DTSTAMP:20260504T025144
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SUMMARY:Slope Gap Distributions of Translation Surfaces (Taylor McAdam\, Pomona College)
DESCRIPTION:Title: Slope gap distributions of translation surfaces \nSpeaker: Taylor McAdam\, Department of Mathematics\, Pomona College \nAbstract: How “random” are the rational numbers? To make sense of this question\, let us consider the set of Farey fractions of level n—that is\, the rational numbers between 0 and 1 with denominator at most n. It turns out that these distribute uniformly in the unit interval as n goes to infinity\, which would suggest they appear to be quite random. However\, we may consider a finer test of randomness by considering the distribution of gaps between consecutive Farey fractions as n tends to infinity. To investigate this\, we will first realize the Farey fractions as the slopes of geodesic paths on the (square) flat torus—a geometric object obtained by gluing the opposite edges of a square together. We will then define the horocycle flow on the space of all flat tori\, which will allow us to study our question about gaps between Farey fractions via a dynamical system. Finally\, we will see how this method can be generalized to study the slope gap distributions for paths on a larger class of geometric objects called translation surfaces and discuss results on the collection of surfaces obtained by gluing together opposite edges of the regular 2n-gon.\n\n\n\n\n\n\nTaylor McAdam graduated with a Bachelor’s degree in mathematics from Harvey Mudd College in 2013 before starting a doctoral program at University of Texas at Austin. In 2017\, she transferred to the University of California San Diego\, where she received her PhD in mathematics in 2019 under the supervision of Amir Mohammadi. She was an NSF Postdoctoral Fellow at Yale University from 2019 to 2023\, before joining the faculty at Pomona College in 2023 as a Visiting Assistant Professor. Her research interests lie at the intersection of dynamical systems\, geometry\, and number theory\, and she is passionate about undergraduate math education and building inclusive mathematical communities.
URL:https://colleges.claremont.edu/ccms/event/slope-gap-distributions-of-translation-surfaces-taylor-mcadam-pomona-college/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231108T161500
DTEND;TZID=America/Los_Angeles:20231108T173000
DTSTAMP:20260504T025144
CREATED:20231020T213110Z
LAST-MODIFIED:20231020T213157Z
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SUMMARY:Lonely Runners and My Favorite Polyhedron (Matthias Beck\, San Francisco State University)
DESCRIPTION:Title: Lonely Runners and My Favorite Polyhedron \nSpeaker: Matthias Beck\, Department of Mathematics\, San Francisco State University \nAbstract: We study the Lonely Runner Conjecture\, conceived by Wills in the 1960’s\, and originally phrased in terms of Diophantine approximation: Given positive integers n_1\, n_2\, …\, n_k\, there exists a positive real number t such that for all 1 ≤ j ≤ k the distance of t n_j to the nearest integer is at least 1/(k+1). This conjecture can be recast in lay terms: if k runners with different (constant) speeds move around a circular track of length 1\, then for each runner there will be a time when they have distance at least 1/k to the others. This (in)famous conjecture in combinatorial number theory is open for k ≥ 7.We will give a brief history of the Lonely Runner Conjecture and some of its variants\, emphasizing a view-obstruction approach by Cusick and recent work by Henze and Malikiosis; our goal is to promote a polyhedral ansatz to the Lonely Runner Conjecture. Our results include affirmative instances that become (quite literally) visible through polyhedral geometry. \nBased on joint work with Serkan Hosten (SF State) and Matthias Schymura (Rostock). \n\n\n\n\n\nMatthias Beck is a professor of mathematics at San Francisco State University and has had visiting positions at SUNY Binghamton\, the Mathematical Sciences Research Institute in Berkeley\, the Max-Planck-Institute in Bonn\, Cornell University\, Vassar College\, and the Freie Universität in Berlin. Matt’s research is in combinatorics and number theory\, in particular\, counting integer points in polyhedra and the application of these enumeration functions to various mathematical topics and problems. He (co-)authored four books and numerous research papers\, many of which feature student coauthors. Matt was honored with the Mathematical Association of America’s Haimo Award for Distinguished College or University Teaching of Mathematics in 2013.x`
URL:https://colleges.claremont.edu/ccms/event/lonely-runners-and-my-favorite-polyhedron-matthias-beck-san-francisco-state-university/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231115T161500
DTEND;TZID=America/Los_Angeles:20231115T173000
DTSTAMP:20260504T025144
CREATED:20231106T190605Z
LAST-MODIFIED:20231106T190605Z
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SUMMARY:Adinkra Heights and Color-Splitting Rainbows (Ursula Whitcher\, American Mathematical Society)
DESCRIPTION:Title: Adinkra Heights and Color-Splitting Rainbows \nSpeaker: Ursula Whitcher\, American Mathematical Society \nAbstract: Adinkras are decorated graphs that encapsulate information about conjectural relationships between fundamental particles in physics. If we color the edges of an Adinkra with a rainbow of shades in a specific order\, we obtain a special curve that we can study usingalgebraic and geometric techniques. We use this structure to characterize height functions on Adinkras\, then show how to compute the same information using data from our rainbow. This talk describes joint work with Amanda Francis. \n\n\n\n\n\nDr. Ursula Whitcher is an associate editor at Math Reviews (MathSciNet)\, a project of the American Mathematical Society\, covering a range of areas from algebraic geometry to history of mathematics. Before joining the AMS\, Dr. Whitcher earned a PhD from the University of Washington\, was a Teaching and Research Postdoctoral Fellow at Harvey Mudd\, and became an associate professor at the University of Wisconsin-Eau Claire. Find Dr. Whitcher’s mathematically inspired poetry and fiction in Asimov’s Science Fiction Magazine\, Analog\, or the Journal of Humanistic Mathematics.
URL:https://colleges.claremont.edu/ccms/event/adinkra-heights-and-color-splitting-rainbows-ursula-whitcher-american-mathematical-society/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20231129T161500
DTEND;TZID=America/Los_Angeles:20231129T173000
DTSTAMP:20260504T025144
CREATED:20231107T015413Z
LAST-MODIFIED:20231107T015413Z
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SUMMARY:“The science of Mathematics is not crystallized into text-books” : The Bryn Mawr Mathematical Journal Club (1896 — 1924)\, (Jemma Lorenat\, Pitzer College)
DESCRIPTION:Title: “The science of Mathematics is not crystallized into text-books” : The Bryn Mawr Mathematical Journal Club (1896 — 1924) \nSpeaker: Jemma Lorenat\, Pitzer College \nAbstract: As mathematics departments in the United States began to shift toward standards of original research at the end of the nineteenth century\, many adopted journal clubs as forums for students to synthesize and share new research. The Bryn Mawr Mathematical Journal Club\, maintained episodically between 1896 and 1924\, began as a supplement to the graduate course offerings. Each semester student and professor participants focused on a single disciplinary area or surveyed what had been published lately. The Notebooks containing these reports were stored on the open shelves of the college library. These collectively composed documents record ways in which graduate students transcribed and interpreted contemporary mathematics. This talk focuses on the entries of Virginia Ragsdale\, in which she formulated research questions\, tested potential strategies\, and pursued novel results in topology. \n\n\n\n\n\nJemma Lorenat is a historian of mathematics at Pitzer College. She enjoys learning about the long nineteenth century\, visualization\, quantification\, ordinary people becoming mathematicians\, food\, and many other things. Her forthcoming book is about how the local environment of Bryn Mawr College shaped mathematical practices there.
URL:https://colleges.claremont.edu/ccms/event/the-science-of-mathematics-is-not-crystallized-into-text-books-the-bryn-mawr-mathematical-journal-club-1896-1924-jemma-lorenat-pitzer-college/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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