seminars:colloquium:y2020-2021
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| + | ====== Colloquium 2020-2021====== | ||
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| + | Unless stated otherwise, colloquia are scheduled for Thursdays 4:15-5:15pm in WH-100E with refreshments served from 4:00-4:15 pm in WH-102. | ||
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| + | Organizers: [[people: | ||
| + | and [[people: | ||
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| + | ----- | ||
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| + | ==== Spring 2021 ==== | ||
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| + | ** A Special Event: ** | ||
| + | Professor Ken Ono (University of Virginia), who is a Phi Beta Kappa Visiting Scholar this year, is virtually visiting our department on March 11-12. He will present three lectures via zoom, | ||
| + | a Math Club Talk for undergraduate and graduate students with interest in mathematics, | ||
| + | a Colloquium Talk for our faculty and graduate students, | ||
| + | and a Public Lecture intended for a general audience. | ||
| + | Details of these talk are given below. | ||
| + | The talks are sponsored by our local Phi Beta Kappa Chapter. | ||
| + | Many thanks to Professor Alex Feingold for organizing this. | ||
| + | |||
| + | **Thursday March 11, 2: | ||
| + | What is the Riemann Hypothesis, and why does it matter? \\ | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | of prime numbers, stating that the nontrivial zeros of the Riemann zeta | ||
| + | function have a “real part” of one-half. A proof of the hypothesis would | ||
| + | be world news and fetch a $1 million Millennium Prize. In this lecture, | ||
| + | Ken Ono will discuss the mathematical meaning of the Riemann hypothesis | ||
| + | and why it matters. Along the way, he will tell tales of mysteries about | ||
| + | prime numbers and highlight new advances. | ||
| + | </ | ||
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| + | |||
| + | **Thursday March 11, 4: | ||
| + | // | ||
| + | //Topic//: Gauss’ Class Number Problem \\ | ||
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| + | <WRAP box 90%> | ||
| + | // | ||
| + | rigorous text in number theory. This book laid the groundwork for modern | ||
| + | algebraic number theory and arithmetic geometry. Perhaps the most | ||
| + | important contribution in the work is Gauss' | ||
| + | quadratic forms, which appears prominently in modern number theory (sums | ||
| + | of squares, Galois theory, rational points on elliptic | ||
| + | curves, | ||
| + | plethora of modern developments in the field, Gauss’s first problem | ||
| + | about quadratic forms has not been optimally resolved. Gauss' | ||
| + | number problem asks for the complete list of quadratic form | ||
| + | discriminants with class number h. The difficulty is in effective | ||
| + | computation, | ||
| + | remains open. To emphasize the subtlety of this problem, we note that | ||
| + | the first case, where h=1, remained open until the 1970s. Its solution | ||
| + | required deep work of Heegner and Stark, and the Fields medal theory of | ||
| + | Baker on linear forms in logarithms. Unfortunately, | ||
| + | generalize to the cases where h>1. In the 1980s, Goldfeld, and Gross and | ||
| + | Zagier famously obtained the first effective class number bounds by | ||
| + | making use of deep results on the Birch and Swinnerton-Dyer Conjecture. | ||
| + | This lecture will tell the story of Gauss’s class number problem, and | ||
| + | will highlight new work by the speaker and Michael Griffin that offers | ||
| + | new effective results by different (and also more elementary) means. \\ | ||
| + | </ | ||
| + | |||
| + | **Friday March 12, 4: | ||
| + | Why does Ramanujan, “The Man Who Knew Infinity”, | ||
| + | \\ **Since this talk is open to the general public, we require registration in advance for this meeting: | ||
| + | [[https:// | ||
| + | After registering, | ||
| + | \\ | ||
| + | |||
| + | <WRAP box 90%> | ||
| + | // | ||
| + | Infinity.” Ramanujan was a self-trained two-time college dropout who | ||
| + | left behind 3 notebooks filled with equations that mathematicians are | ||
| + | still trying to figure out today. He claimed that his ideas came to him | ||
| + | as visions from an Indian goddess. This lecture gives many reasons why | ||
| + | Ramanujan matters today. The answers extend far beyond his legacy in | ||
| + | science and mathematics. The speaker was an Associate Producer of the | ||
| + | film “The Man Who Knew Infinity” (starring Dev Patel and Jeremy Irons) | ||
| + | about Ramanujan. He will share several clips from the film in the | ||
| + | lecture, and will also tell stories about the production and promotion | ||
| + | of the film. | ||
| + | </ | ||
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| + | ----- | ||
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| + | ----- | ||
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| + | Archive: | ||
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| + | /* * [[http:// | ||
| + | /* * [[http:// | ||
| + | * [[seminars: | ||
| + | * [[seminars: | ||
| + | * [[seminars: | ||
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