| Date: | May 1, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alice Mark |
| Title: | Local Invariance for Quadratic Forms |
| Abstract: | We'll talk about the use of the genus in the classification of reflective integral lattices. |
| Date: | April 24, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Edna Jones |
| Title: | Clifford algebras and Mobius transformations |
| Abstract: | I will talk about Clifford algebras and how we can use them to create Mobius transformations in hyperbolic n-space. |
| Date: | April 17, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alex Kontorovich |
| Title: | Vinberg's algorithm (Part 5) |
| Abstract: | I'll talk about Vinberg's algorithm. |
| Date: | April 10, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alex Kontorovich |
| Title: | Vinberg's algorithm (Part 4) |
| Abstract: | I'll talk about Vinberg's algorithm. |
| Date: | April 3, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alex Kontorovich |
| Title: | Vinberg's algorithm (Part 3) |
| Abstract: | I'll talk about Vinberg's algorithm. |
| Date: | March 27, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alex Kontorovich |
| Title: | Vinberg's algorithm (Part 2) |
| Abstract: | I'll talk about Vinberg's algorithm. |
| Date: | March 13, 2019 |
|---|---|
| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alex Kontorovich |
| Title: | Vinberg's algorithm |
| Abstract: | I'll talk about Vinberg's algorithm. |
| Date: | March 6, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Brooke Logan Ogrodnik |
| Title: | Constructing A Dirichlet Domain in Hyperbolic Three Space |
| Abstract: | I will work through an example of constructing a Dirichlet Domain in Hyperbolic Three Space for a discrete subgroup of SL(2,C). In the talk I will point out similarities and differences between a known example in the upper half plane. |
| Date: | February 27, 2019 |
|---|---|
| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alexander Walker |
| Title: | The Quadratic and Number Field Sieves |
| Abstract: | The quadratic sieve and number field sieve are the two fastest factoring algorithms known today. In this talk, I'll describe in detail how the quadratic sieve works and remind you about all the horrible things that can happen when we try to do computations using number fields. I will also talk about how these two algorithms developed out of similar, simpler factoring algorithms (like CFRAC and the linear sieve) from the earlier twentieth century. |
| Date: | February 20, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | George Hauser |
| Title: | The theta function as an automorphic form on the metaplectic group |
| Abstract: | The theta function is a basic example of a modular form of half-integral weight. As such, its transformation law is delicate, since care must be taken in choosing a branch cut for the square root. The metaplectic group is a double cover of SL(2,R). I will explain how it is natural to look at the theta function as an automorphic form on the metaplectic group, and how this conceptual arrangement simplified the transformation law for the theta function. |
| Date: | February 13, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alice Mark |
| Title: | Continued Fractions in the Heisenberg Group |
| Abstract: | This is a talk about Lukyanenko & Vandehey's paper on continued fractions on the Heisenberg group. Why do this? The Heisenberg group is a natural place to look for higher dimensional analogues to classical continued fractions because in much the same way that the real or complex numbers plus a point at infinity are the boundaries of 2- and 3-dimensional real hyperbolic space, the 3-dimensional Heisenberg group plus a point at infinity is the boundary of the complex hyperbolic plane. |
| Date: | January 30, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Edna Jones |
| Title: | Inversive Coordinates and Descartes Circle Theorem |
| Abstract: | Descartes circle theorem describes a relationship between the curvatures of four mutually tangent circles. After introducing inversive coordinates, I will give a proof of Descartes circle theorem using inversive coordinates. |
| Date: | January 23, 2019 |
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| Time: | 11:00 A.M. |
| Place: | Hill 423 |
| Speaker: | Alex Karlovitz |
| Title: | Maass Cusp Forms and Hejhal’s Algorithm |
| Abstract: | Maass forms are certain eigenfunctions of the hyperbolic Laplacian on the upper half plane. They must also be automorphic functions with respect to some Fuchsian group Gamma. It turns out that restricting our attention to Maass forms in L^2(Gamma\H) admits a discrete spectrum for the Laplacian. Much current research is devoted to computing these eigenvalues. In this talk, I will define Maass forms and Maass cusp forms for SL(2, Z), and I will explain how to derive a nice Fourier expansion for the cusp forms. Then, I will describe an algorithm due to Dennis Hejhal for computing Laplacian eigenvalues of these functions. |