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DTSTART;TZID=America/Los_Angeles:20220906T121500
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DTSTAMP:20260418T220613
CREATED:20220811T001752Z
LAST-MODIFIED:20220902T173415Z
UID:2779-1662466500-1662469800@colleges.claremont.edu
SUMMARY:Monodromy groups of Belyi Lattes maps (Edray Goins\, Pomona College)
DESCRIPTION:An elliptic curve $ E: y^2 + a_1 \\, x \\, y + a_3 \\, y = x^3 + a_2 \\, x^2 + a_1 \\, x + a_6 $ is a cubic equation which has two curious properties: (1) the curve is nonsingular\, so that we can draw tangent lines to every point $ P = (x\,y) $ on the curve; and (2) the collection of complex points\, namely $ E(\mathbb C) $\, forms an abelian group under a certain binary operation $ \bigoplus: E(\mathbb C) \times E(\mathbb C) \to E(\mathbb C) $.   In particular\, for every positive integer $N$\, the map $ P \mapsto [N] P $ which adds a point $ P \in E(\mathbb C) $ to itself $N$ times is a group homomorphism.   A rational map $\gamma: \mathbb P^1(\mathbb C) \to \mathbb P^1(\mathbb C) $ from the Riemann Sphere to itself is said to be a Latt\`{e}s Map if there are “well-behaved” maps $ \phi: E(\mathbb C) \to \mathbb P^1(\mathbb C) $ and $\psi: E(\mathbb C) \to E(\mathbb C) $ such that $\gamma \circ \phi = \phi \circ \psi$.  We are interested in those Latt\`{e}s Maps $\gamma$ which are also Bely\u{\i} Maps\, that is\, the only critical values are $ 0 $\, $ 1 $\, and $ \infty $.  Work of Zeytin classifies all such maps: For example\, if $ E: y^2 = x^3 + 1 $ then $ \phi: (x\,y) \mapsto (y+1)/2 $ while $\psi = [N] $ for some positive integer $N$.\n\nWe would like to know more about Bely\u{\i} Latt\`{e}s Maps $\gamma$.  What can we say about such maps?  What are their Dessin d’Enfants?  In some cases\, this is a bipartite graph with $ 3 \\, N^2 $ vertices.  What are their monodromy groups? Sometimes this is a group of size $ 3 \\, N^2 $.  In this talk\, we explain the complete answers to these questions\, exploiting the relationship between fundamental groups of Riemann surfaces and Galois groups of function fields.  This work is conducted as part of the Pomona Research in Mathematics Experience (DMS-2113782).
URL:https://colleges.claremont.edu/ccms/event/monodromy-groups-of-belyi-lattes-maps-edray-goins-pomona-college/
LOCATION:Estella 1021 (Emmy Noether Room)\, Pomona College\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20220907T161500
DTEND;TZID=America/Los_Angeles:20220907T173000
DTSTAMP:20260418T220613
CREATED:20220828T210059Z
LAST-MODIFIED:20220906T155701Z
UID:2796-1662567300-1662571800@colleges.claremont.edu
SUMMARY:Poster Session Fall 2022
DESCRIPTION:CLAREMONT CENTER for the MATHEMATICAL SCIENCES\nFall 2022 Poster Session \n  \n\n\n\n\n\n\nTitle\nSpeaker(s)\n\n\nA New Basis for k-Local Class Functions\nHannah Friedman\n\n\nA Quantile Deffuant-Weisbuch Model of Opinion Dynamics\nJulianna Schalkwyk\, Hector Tierno\n\n\nAnalyzing Chromatin Immunoprecipitation (ChIP-Seq) Between-Sample Normalization Techniques through the Lens of their Biological Assumptions\nSara Colando\n\n\nCharacterizing Missing Traffic Stop Data\nSaatvik Kher\, Kyle Torres\n\n\nComputationally Modeling Transcranial Ultrasound Propagation for the Optimization of Drug Delivery to the Brain using Sonosensitive Liposomes\nRuth Gale\n\n\nDistributed Non-negative Matrix Factorization (DNMFX) with JAX\nAlicia Lu\n\n\nExploring the HCV\nOscar Scholin\, Graham Hirsch\n\n\nGeometric characteristics of symmetric numerical semigroups in the Kunz cone\nLily Natasha Wartman\n\n\nHorizontal dipole excitations of hydrodynamic electrons in graphene\nKausik Das\n\n\nKaczmarz for Time-Varying Noise and Corruption\nNestor Coria\, Jaime Pacheco\n\n\nMonodromy Groups of Belyi Lattes Maps\nZoë Batterman\, Eben Semere\n\n\nMonotonicity Failure in Ranked Choice Voting\nRylie Weaver\n\n\nOptimization of drug delivery in the brain\nStanley Su\n\n\nOptimization of the delivery of Ropinirole across the blood-brain-barrier\nStanley Su\n\n\nPartially Ordered Sets\nMehek Mehra\n\n\nQuantum Electrodynamics and Electron Scattering\nIshan Varma\n\n\nRates of Approximation by ReLU Shallow Neural Networks\nTong Mao\n\n\nSimulations and extensions of bounded confidence opinion dynamics model with zealots\nIan de Marcellus\n\n\nStochastic Models of Zoonotic Avian Influenza with Multiple Hosts\, Environmental Transmission\, and Migration in the Natural Reservoir\nKaia Smith\n\n\nSum and Product Game\nMariam Abu-Adas\n\n\nTensor Methods and Models for Medical Imaging\nNoah Limpert\, Toby Anderson
URL:https://colleges.claremont.edu/ccms/event/poster-session-fall-2022/
LOCATION:Margaret Fowler Garden\, Scripps College\, Claremont\, CA\, 91711
CATEGORIES:Colloquium,Special Event
GEO:34.103917;-117.709694
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DTSTART;TZID=America/Los_Angeles:20220908T160000
DTEND;TZID=America/Los_Angeles:20220908T170000
DTSTAMP:20260418T220613
CREATED:20220905T060933Z
LAST-MODIFIED:20230816T041748Z
UID:2824-1662652800-1662656400@colleges.claremont.edu
SUMMARY:Factorization theorems of Backward Shifts and Nuclear Maps (Asuman Aksoy\, CMC)
DESCRIPTION:The theory of compact linear operators between Banach spaces has a classical core and is familiar to many. Perhaps lesser known is the factorization of compact maps through a closed subspace of \(c_0\) [2]. This factorization theorem has a number of important connections and consequences analogous to how the ideals of continuous linear operators factoring compactly through \(\ell^p\)-spaces \((1\leq p < \infty)\) (see [1] and the references therein). In this talk\, even though hypercyclic operators are not compact\, we consider operator ideals generated by hypercyclic backward weighted shifts and examine their factorization properties. (Joint work with Yunied Puig)\n\n\n\nFourie\, Jan H. Injective and surjective hulls of classical \(p\)-compact operators with application to unconditionally \(p\)-compact operators. Studia Math.  240  (2018)\, no. 2\, 147–159. MR3720927\nTerzioğlu\, T. A characterization of compact linear mappings. Arch. Math. (Basel) 22 (1971)\, 76–78. MR0291865
URL:https://colleges.claremont.edu/ccms/event/factorization-theorems-of-backward-shifts-and-nuclear-maps-asuman-aksoy-cmc/
LOCATION:Roberts North 105\, CMC\, 320 E. 9th St.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Analysis Seminar
ORGANIZER;CN="Asuman Aksoy":MAILTO:asuman.aksoy@claremontmckenna.edu
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