Past Events

Visit: Prof. Benjamin Burton

2019-03-17 to 2019-03-23

Visit: Prof. Benjamin Burton

[CANCELLED] Visit: Prof. Brandy Doleshal

2019-02-26 to 2019-03-05
Visit: Dr. Brandy Doleshal

Visit: Prof. Brandy Doleshal

[Geometry, Topology and Dynamics Seminar] Viazovska's work on the sphere packing problem and some recent developments in number theory by Dr. Dan Romik (UC Davis)

2019-02-25
Lab 3, B700
Abstract: The sphere packing problem in d dimensions asks for the densest packing of spheres in d-dimensional Euclidean space R^d. Prior to 2016, the problem had only been solved in dimensions 2 and 3 (with the solution in dimension 3 being Hales's famously complicated solution to Kepler's conjecture), and solutions in most other dimensions were thought to be out of reach, except for dimensions 8 and 24 where overwhelming numerical and theoretical evidence supported the conjectures pointing at specific lattices as the optimal packings. In a breakthrough in 2016, Maryna Viazovska published a stunning proof for the 8-dimensional case, followed up shortly with a proof for the 24-dimensional case with several coauthors. The solutions work by using a previous reduction of the problem (due to Henry Cohn and Noam Elkies) to a problem in harmonic analysis, and ingeniously solving that analysis problem using number-theoretic tools - specifically, the mathematics of modular forms.
 
In this talk I will give a quick survey of these developments and the beautiful new challenges and opportunities that they open up for attacking this classical geometry problem. I will also discuss my own recent results on infinite series representations for the Riemann xi function and explain how Viazovska's work, which appears not strongly related to the problem I was studying, nonetheless provided me with useful inspiration.

[Geometry, Topology and Dynamics Seminar] Ramified covering maps of spheres and arboreal polygons by Dr. Michael Kapovich (UC Davis)

2019-02-21
Lab 3, B700

[Geometry, Topology and Dynamics Seminar]  Ramified covering maps of spheres and arboreal polygons  by Dr. Michael Kapovich (UC Davis)

Visit: Prof. Dan Romik, UC Davis

2019-02-21 to 2019-03-06

Visit: Prof. Dan Romik, UC Davis

[Geometry, Topology and Dynamics Seminar] The Kakimizu complex of Seifert fibered spaces by Dr. Jennifer Schultens (UC Davis)

2019-02-20
Lab 3, B700

[Geometry, Topology and Dynamics Seminar] Dr. Jennifer Schultens (UC Davis) will talk about the Kakimizu Complex of Seifert fibered spaces.

[Geometry, Topology and Dynamics Seminar] Alternating knots are rare by Dr. Harrison Chapman (Colorado State University)

2019-02-18
Lab 3, B700

[Geometry, Topology and Dynamics Seminar]  Dr. Harrison Chapman from Colorado State University will give a talk titled Alternating knots are rare.

Visit: Dr. Harrison Chapman, Colorado State University

2019-02-17 to 2019-02-26

Visit: Dr. Harrison Chapman, Colorado State University

Profs. Michael Kapovich and Jennifer Schultens visit

2019-02-17 to 2019-02-24

Profs. Michael Kapovich and Jennifer Schultens visit

[Geometry, Topology and Dynamics Seminar] Neck-pinching of CP^1-structures by Dr. Shinpei Baba (Osaka University)

2019-01-30
Lab 3, B700

Abstract: A CP^1-structure is a geometric structure on a (compact oriented) surface S  and its holonomy is a homomorphism from the fundamental group of the surface into PSL(2, C).  Moreover it corresponds to a holomorphic quadratic differential on a Riemann surface. 

We consider a path C_t of CP^1-structures on S  such that C_t diverges to infinity in its deformation space and yet its holonomy converges.  We describe its asymptotic behavior of C_t under the assumption the Riemann surface structure on C_t is pinched along a single loop.  

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