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DTSTART;TZID=America/Los_Angeles:20240207T161500
DTEND;TZID=America/Los_Angeles:20240207T173000
DTSTAMP:20260503T042528
CREATED:20240201T010113Z
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SUMMARY:Shrinkage Estimation for Causal Inference and Experimental Design (Evan T. R. Rosenman)
DESCRIPTION:Title: Shrinkage Estimation for Causal Inference and Experimental Design \nSpeaker: Evan T. R. Rosenman\, Assistant Professor of Statistics\, Claremont McKenna College \nAbstract: Passive collection of observational data — in settings such as medicine\, insurance\, and e-commerce — is a ubiquitous feature of modern life. For statisticians\, these ever-proliferating datasets are both promising and perilous. Observational data often contain rich information about the causal effects of novel treatments\, such as a new vaccine or drug regimen. Yet\, because assignment to treatment is not randomized within these data\, one can never guarantee that treated and untreated units are comparable. Consequently\, causal effects derived from observational studies often suffer from bias. The applied literature contains myriad examples of treatments that seemed promising in observational data\, only to be overturned by later\, higher-quality studies. \nHow might we make headway\, given these challenges? One approach is to couple observational data with randomized trials. In this talk\, I will consider how to develop estimators to merge causal effect estimates obtained from observational and experimental datasets\, when the two data sources measure the same treatment. I will primarily operate in the Empirical Bayes (EB) framework. EB procedures\, rooted in the work of Charles Stein and the renowned James-Stein estimator\, offer principled\, data-driven methods for reconciling competing estimates of the same quantity. I will discuss two techniques for deriving EB estimators that effectively merge observational and experimental causal estimates. Additionally\, I will explore the potential contribution of these concepts to improving the efficiency of prospective randomized trials. Simple algorithms\, leveraging numerical integrals\, will be highlighted for making more informed recruitment and treatment assignment decisions within the experimental setup.\n\n\n\n\n\nEvan Rosenman is an Assistant Professor of Statistics in the Claremont McKenna Department of Mathematical Sciences. His research focuses primarily on problems in data science and causal inference\, with applications to political science and public health. He is particularly intrigued by problems involving hybridizing observational and experimental data to better estimate causal effects\, and by applications in modern electioneering\, such as ecological inference and prediction calibration. He earned his PhD in Statistics from Stanford University and completed a postdoctoral fellowship at the Harvard Data Science Initiative.
URL:https://colleges.claremont.edu/ccms/event/shrinkage-estimation-for-causal-inference-and-experimental-design-evan-t-r-rosenman/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240214T161500
DTEND;TZID=America/Los_Angeles:20240214T173000
DTSTAMP:20260503T042528
CREATED:20240210T024434Z
LAST-MODIFIED:20240210T024434Z
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SUMMARY:Mirror Symmetry and Zeta Values (Sheel Ganatra\, USC)
DESCRIPTION:Title: Mirror Symmetry and Zeta Values \nSpeaker: Sheel Ganatra\, University of Southern California \nAbstract: Mirror symmetry is a conjectural correspondence\, born out of ideas in string theory\, between two geometries of very different nature. In its earliest mathematical appearance\, mirror symmetry was used to make predictions for certain numerical measurements of one space in terms of utterly different calculations on a mirror space. Mysteriously\, certain famous arithmetic constants\, the Riemann zeta values\, were repeatedly observed to appear in the transformation taking measurements on one side to measurements on the mirror side.  I will survey these ideas and then present joint work with Abouzaid\, Iritani\, and Sheridan explaining a geometric origin for the appearance of these constants in mirror symmetry. \n\n\n\n\n\nSheel Ganatra is an Associate Professor at the University of Southern California. Prior to coming to USC in 2016\, he completed his PhD at MIT with Denis Auroux in 2012 (two years of which were on exchange at UC Berkeley) and spent 4 years as a Szegö Assistant Professor and NSF postdoctoral Fellow at Stanford. His research interests include symplectic geometry and mirror symmetry\, and he is the recipient of an NSF Career Award and a Simons Fellowship.
URL:https://colleges.claremont.edu/ccms/event/mirror-symmetry-and-zeta-values-sheel-ganatra-usc/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20240221T161500
DTEND;TZID=America/Los_Angeles:20240221T173000
DTSTAMP:20260503T042528
CREATED:20240202T200558Z
LAST-MODIFIED:20240202T200558Z
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SUMMARY:Evolution of an Intriguing Recreational Math Problem (Shawn McMurran\, California State University San Bernardino)
DESCRIPTION:Title: Evolution of an Intriguing Recreational Math Problem \nSpeaker: Shawn McMurran\, California State University San Bernardino \nAbstract: Besides being popular and entertaining\, recreational mathematics problems are often of historical interest. In this presentation we will highlight the origin and evolution of one such simply stated yet deep problem. The problem emerged during the eighteenth century tucked into a primarily standard arithmetic text. Over the next two centuries\, several notable names contributed to a growing collection of extensions\, generalizations\, and solution strategies. In more recent years\, relatives of this versatile problem have remained ubiquitous. It is likely that most audience members are familiar with at least one of its incarnations. During our journey\, opportunities will be provided for the audience to engage with the problem and some of its variations. \n\n\n\n\n\nShawn McMurran is a professor of mathematics at California State University San Bernardino. She earned her PhD in mathematics from UC Riverside with a background in PDEs. Current areas of interest include mathematics education and history of mathematics. She and her colleague Jim Tattersall have enjoyed many years of collaboration on math history projects\, including the subject of this presentation.
URL:https://colleges.claremont.edu/ccms/event/evolution-of-an-intriguing-recreational-math-problem-shawn-mcmurran-california-state-university-san-bernardino/
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:20240228T161500
DTEND;TZID=America/Los_Angeles:20240228T173000
DTSTAMP:20260503T042528
CREATED:20240222T005317Z
LAST-MODIFIED:20240222T005317Z
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SUMMARY:A Group-Theoretic Ax-Katz Theorem (Pete L. Clark\, University of Georgia)
DESCRIPTION:Title: A Group-Theoretic Ax-Katz Theorem \nSpeaker: Pete L. Clark\, University of Georgia \nAbstract: The Chevalley-Warning Theorem is a result from 1935 asserting that the number of solutions to a low degree polynomial system over a finite field is divisible by the characteristic of the field.  It is an important result — it includes a conjecture of Artin and Dickson from the 1920’s — but it is not difficult to prove: the original proof is about three pages.  In 1964 James Ax gave a completely elementary ten line proof.   In the same paper\, Ax showed that as the number and degrees of the polynomials are held fixed and the number of variables increases\, not only is the size of the solution set divisible by p but by higher and higher powers of p.  The best possible p-adic divisibility here was given in 1971 by Nicholas Katz.  Katz’s proof is at a much higher level: you need specialist knowledge in the right subfields of number theory to understand it.  Simpler proofs were found later\, but none fulfills the fantasy of generalizing Ax’s ten line proof of Chevalley-Warning. \nA 2021 work of Aichinger-Moosbauer develops a fully fledged calculus of finite differences for maps between commutative groups and uses it to give a purely group-theoretic generalization of Chevalley-Warning. Nicholas Triantafillou and I have used and extended this work: up to a few black boxes (where most of the content is indeed hidden) we give a ten line proof of a group-theoretic analogue of Ax-Katz that “qualitatively fulfills my fantasy.”\n\n\n\n\n\nIn (North)west Philadelphia was Pete L. Clark born and raised.  He received undergraduate and masters degrees from the University of Chicago and a PhD from Harvard University.  He has worked in the Mathematics Department at the University of Georgia since 2006\, where he was the Graduate Coordinator from 2016-2019 and where he is now the Principal Honors Advisor.  When time permits he is an avid reader\, and his favorite authors include Ralph Ellison\, Jonathan Franzen\, Kazuo Ishiguro\, Carmen Maria Machado and Lorrie Moore.
URL:https://colleges.claremont.edu/ccms/event/a-group-theoretic-ax-katz-theorem-pete-l-clark-university-of-georgia/
LOCATION:Argue Auditorium\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Colloquium
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