| Date: | December 6, 2018 |
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| Time: | 11:00 - 11:50 A.M. |
| Place: | Hill 425 |
| Speaker: | Edna Jones |
| Title: | Continued Fractions and Ergodic Theory |
| Abstract: | I will talk about how ergodic theory can be used to obtain some interesting results about continued fractions, such as how frequently a given positive integer appears in the continued fractions of most real numbers. |
| Date: | November 15, 2018 |
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| Time: | 11:00 - 11:50 A.M. |
| Place: | Hill 425 |
| Speaker: | Brooke Logan Ogrodnik |
| Title: | Selberg's Upper Bound Sieve |
| Abstract: | In this talk, I will discuss a brief history of Selberg's Upper Bound Sieve. The talk will then apply this sieve in different situations. Depending on time, sequences of primes and primes in arithmetic progressions will be discussed. |
| Date: | November 1, 2018 |
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| Time: | 11:00 - 11:50 A.M. |
| Place: | Hill 425 |
| Speaker: | Louis Gaudet |
| Title: | The Gauss Circle Problem |
| Abstract: | The Gauss circle problem is to determine an asymptotic formula for the number of integer lattice points contained in a circle centered at the origin as the radius tends to infinity. While the main term is easily determined by a geometric argument, the exact order of magnitude of the error is still today an open problem. I will discuss and prove several main results known about the problem: the classical improvement on the error bound, a lower bound on the error, and an explicit formula. These results nicely demonstrate some fundamental analytic techniques in number theory. |
| Date: | October 18, 2018 |
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| Time: | 11:00 - 11:50 A.M. |
| Place: | Hill 425 |
| Speaker: | George Hauser |
| Title: | L-functions, the explicit formula, and the highest-lowest zero |
| Abstract: | The celebrated explicit formula for the Riemann zeta function relates sums over prime powers to sums over zeta’s zeros. A similar explicit formula exists for general L-functions. In this expository talk I will explain the explicit formula, and show how it applies to the problem of the “highest-lowest zero” of L-functions: how large can the imaginary part be of the first critical zero of an L-function? The answer to this question is most likely that the Riemann zeta function has the highest-lowest zero, and while this is proved in many cases, it is not known in full generality. |
| Date: | October 4, 2018 |
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| Time: | 11:00 - 11:50 A.M. |
| Place: | Hill 425 |
| Speaker: | Surya Teja Gavva |
| Title: | Erdos Multiplication Table Problem |
| Abstract: | I will discuss the problem of counting integers obtained by multiplying 1,2,...,N to 1,2,.,.,N. This simple looking problem requires a good understanding of distribution of prime factors and divisors of integers. We will see how probabilistic ideas help us to get an estimate of the order of magnitude of the count. The problem of finding asymptotics is still open! |
| Date: | September 20, 2018 |
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| Time: | 11:00 - 11:50 A.M. |
| Place: | Hill 425 |
| Speaker: | Matthew Welsh |
| Title: | Equidistribution of Roots of a Quadratic Congruence |
| Abstract: | See the linked PDF. |