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Tom Weston, Associate Professor |
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| Personal Webpage |
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| Office | LGRT 1122 | | Phone | (413) 545-6037 | | Fax | (413) 545-1801 | | Email | weston <at> math.umass.edu | |
| Mailing Address |
| Department of Mathematics and Statistics |
| Lederle Graduate Research Tower |
| University of Massachusetts |
| Amherst, MA 01003-9305 |
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| Courses |
| Honors Calculus I |
| Math 131H (TuTh 9:30 - 10:45 am, LGRT 117) |
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| Introduction to Abstract Algebra I |
| Math 411.1 (TuTh 11:15 - 12:30 pm, LGRT 113) |
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| Algebraic Number Theory |
| Math 791N (TuTh 2:30 - 3:45 pm, LGRT 1322) | | |
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| Education | | Ph.D. | Harvard University, 2000 |
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| | S.M. | Harvard University, 1997 |
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| | S.B. | Massachusetts Institute of Technology, 1996 |
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| Research Interests: Arithmetic algebraic geometry, Iwasawa theory of modular forms, deformation theory of Galois representations |
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| Professor Weston studies the interplay between L-functions and certain arithmetic objects known as Selmer groups. Selmer groups are generalizations of ideal class groups and the group of rational points on an elliptic curve which distill the information contained in p-adic representations of the absolute Galois group. He has used such relations to enlarge dramatically the number of cases in which one can precisely compute universal deformation rings as in the work of Wiles. Jointly with Robert Pollack of Boston University, he also studies the behavior of L-functions and Selmer groups of modular forms in certain p-adic analytic families. In many cases they are able to show that one can use values of the L-functions (which are relatively computable) to compute Selmer groups (which are a priori very difficult to compute). |
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| Selected Publications |
| M. Emerton, R. Pollack, T. Weston, Variation of Iwasawa invariants in Hida families, Inventiones Mathematicae 163 (2006), 523-580. |
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| T. Weston, Iwasawa invariants of Galois deformations, Manuscripta Mathematica 118 (2005), 161-180. |
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| T. Weston, Unobstructed modular deformation problems, American Journal of Mathematics 126 (2004), 1237-1252. |
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| T. Weston, Geometric Euler systems for locally isotropic motives, Compositio Mathematica 140 (2004), 317-332. |
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| T. Weston, Algebraic cycles, modular forms and Euler systems, Journal fur die Reine und Angewandte Mathematik 543 (2002), 103-145. |
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