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SUMMARY:CCMS Colloquium: Fractal Cohomology of the Ternary Cantor Set: An Invitation to the Imaginarium of Complex Dimensions — Shanna Dobson (Harvey Mudd College)
DESCRIPTION:Abstract: We present our program of geometrizing cohomology on a totally disconnected space through the intrinsic Cantor function and the cohomological complex dimensions of the ternary Cantor set. The Cantor set is an uncountable\, self-similar set of measure zero; yet beneath this apparent “dust” lies a remarkably rich geometry across scales. We show how cohomological information can be organized and transported through this multiscale geometry\, giving rise to nontrivial local and global fractal cohomology groups. \nWe describe how this multiscale geometry gives rise to a hierarchy of cohomological complex dimensions and indicate the resulting connections among geometry\, analysis\, and cohomology. A dust of points can carry a coherent geometry across every scale—and that geometry is reflected in a hierarchy of complex dimensions. This talk is based on forthcoming joint work with Michel L. Lapidus. \nBio: Dr. Shanna Dobson is a Visiting Assistant Professor of Mathematics at Harvey Mudd College. She received her PhD in Mathematics (summa cum laude) from the University of California\, Riverside\, where she studied fractal and arithmetic geometry\, and category theory. Dr. Dobson’s graduate research was supported by a National Science Foundation Mathematical Sciences Graduate Research Fellowship\, and she participated in the Institute for Advanced Study Women and Mathematics Program and Ambassadorship. She also teaches mathematics at Cal State LA and ArtCenter College of Design in Pasadena. Her teaching emphasizes creativity\, inquiry-based learning\, and helping students build confidence and curiosity in mathematics. Dr. Dobson is the founder of the AWM research network Women\, Art\, and Mathematics (WAAM)\, and currently serves as Chair of the Southern California–Nevada Section of the Mathematical Association of America\, and Associate Editor of the Anneli Lax New Mathematical Library. \n\n\n\nFor questions about the event\, please contact your CCMS Colloquium chairs: \nProf. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu) \nFor logistical questions\, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu)\, the CCMS Colloquium Assistant.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-fractal-cohomology-of-the-ternary-cantor-set-an-invitation-to-the-imaginarium-of-complex-dimensions-shanna-dobson-harvey-mudd-college/
LOCATION:Burkle 16\, Claremont Graduate University\, 1021 N. Dartmouth Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Qidi Peng":MAILTO:Qidi.Peng@cgu.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20261118T161500
DTEND;TZID=America/Los_Angeles:20261118T171500
DTSTAMP:20261022T211901Z
CREATED:20261022T211901Z
LAST-MODIFIED:20261022T211901Z
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SUMMARY:CCMS Colloquium: Non-Vanishing of L-Functions — Alexander Dunn (Georgia Institute of Technology)
DESCRIPTION:Abstract: Dirichlet’s 1837 proof of his theorem on primes in arithmetic progressions depended on the non-vanishing of \(L(1\,\chi)\) for nonprincipal characters. The Birch and Swinnerton-Dyer conjecture relates the rank of an elliptic curve to the order of vanishing of its \(L\)-function at the central point. Determining whether an individual central value vanishes can be difficult\, but averaging over families allows us to prove non-vanishing for many members at once. \nI will discuss this approach for cubic and quartic Hecke \(L\)-functions and the predictions from random matrix theory. Recent joint work establishes unconditionally that a positive proportion of the members of certain families have nonzero central values. In the quartic case\, our methods also show that a positive proportion of the curves \(y^2=x^3-qx\)\, with squarefree \(q\in\mathbb Z[i]\) ordered by norm\, have rank zero over \(\mathbb Q(i)\). \nThe cubic work is joint with Chantal David\, Alexandre de Faveri\, and Joshua Stucky. The quartic work is joint with Cruz Castillo and Alexandre de Faveri. \n\n\n\nFor questions about the event\, please contact your CCMS Colloquium chairs: \nProf. Robert Cass (Robert.Cass@ClaremontMcKenna.edu) or Prof. Qidi Peng (Qidi.Peng@cgu.edu) \nFor logistical questions\, contact Maxwell Kooiker (Maxwell.Kooiker@cgu.edu)\, the CCMS Colloquium Assistant.
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-non-vanishing-of-l-functions-alexander-dunn-georgia-institute-of-technology/
LOCATION:Burkle 16\, Claremont Graduate University\, 1021 N. Dartmouth Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Qidi Peng":MAILTO:Qidi.Peng@cgu.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20261119T161500
DTEND;TZID=America/Los_Angeles:20261119T171500
DTSTAMP:20260929T162313Z
CREATED:20260929T162313Z
LAST-MODIFIED:20260929T162313Z
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SUMMARY:The 17th Atul Vyas Memorial Lecture in Mathematics — Alexander Dunn (Georgia Institute of Technology)
DESCRIPTION:Atul Vyas was an outstanding CMC student who was majoring in Mathematics and Physics. He tragically lost his life in a train crash that occurred on September 12\, 2008 in Chatsworth\, California. The Mathematical Sciences Department at CMC fondly remembers Atul as someone who was equally excited by the power of mathematical abstraction and the possibilities for its applications. \nIn memory of Atul\, the CMC Mathematical Sciences Department hosts a yearly lecture series\, aimed at a general audience\, on the Creative Application of Abstract Mathematical Ideas.
URL:https://colleges.claremont.edu/ccms/event/the-17th-atul-vyas-memorial-lecture-in-mathematics-alexander-dunn-georgia-institute-of-technology/
ORGANIZER;CN="Robert Cass":MAILTO:rcass@cmc.edu
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20261209T161500
DTEND;TZID=America/Los_Angeles:20261209T171500
DTSTAMP:20260903T024009Z
CREATED:20260903T024009Z
LAST-MODIFIED:20260903T024009Z
UID:10002248-1796832900-1796836500@colleges.claremont.edu
SUMMARY:CCMS Colloquium — Trung (Average) Phan (Pitzer\, Scripps)
DESCRIPTION:
URL:https://colleges.claremont.edu/ccms/event/ccms-colloquium-trung-average-phan-pitzer-scripps/
LOCATION:Burkle 16\, Claremont Graduate University\, 1021 N. Dartmouth Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
ORGANIZER;CN="Qidi Peng":MAILTO:Qidi.Peng@cgu.edu
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