| Noga Alon, Princeton University and Tel Aviv University | Noga Alon, Princeton University and Tel Aviv University | GORE 104 | Title: List Coloring
<br><br>
Abstract: The list chromatic number of a graph G is the minimum k so that for every
assignment of a list of k colors to any vertex of G there is a
vertex coloring assigning to each vertex a color from its list, so that
adjacent vertices get distinct colors. This notion was introduced by
Vizing and by Erdos, Rubin and Taylor in the late 70s and its
study combines combinatorial, probabilistic and algebraic techniques.
Its natural extension to hypergraphs is closely related to questions in
Euclidean Ramsey Theory.
I will discuss several old and new problems and results in the area focusing
on a recent work with Briceno, Chandgotia, Magazinov and Spinka
motivated by questions in statistical physics regarding vertex colorings
of the d-dimensional lattice. | 11/8/2019 8:30:00 PM | 11/8/2019 9:30:00 PM | False | |
| Ridgway Scott from University of Chicago | Ridgway Scott from University of Chicago | GORE 104 | Title: Automated Modeling with FEniCS<br><br>
Description: The FEniCS Project develops both fundamental software components
and end-user codes to automate numerical solution of partial
differential equations (PDEs). FEniCS enables users to translate
scientific models quickly into efficient finite element code and
also offers powerful capabilities for more experienced programmers.
FEniCS and other automated software are catalyzing a change for
PDEs similar to the one that Matlab did for linear algebra.<br><br>
FEniCS uses the variational formulation of PDEs as a language to
define models. We will explain the variational formulations for
simple problems and then show how they can be extended to simulate
fluid flow. The variational formulation also provides a firm
theoretical foundation for understanding PDEs. We argue that
combining the theory with practical coding provides a way to teach
PDEs, their numerical solution, and associated modeling without
requiring extensive mathematical prerequisites. We demonstrate
that this approach requires no background in PDEs or finite
elements, only multi-variate calculus.<br><br>
FEniCS also provides a productive platform for research. We will
present examples where it has been used to answer questions that
would have required months of programming using traditional
techniques.
| 10/18/2019 7:30:00 PM | 10/18/2019 8:30:00 PM | False | |
| Fan Chung, University of California, San Diego | Fan Chung, University of California, San Diego | GORE 104 | Title: Many Facets of Hypercubes
<br><br>
Description: We will discuss several problems concerning the n-cube and briefly survey some recent developments.
We will cover a variety of topics,
including Ramsey and Turan problems for hypercubes, isoperimetric properties of hypercubes, routing in hypercubes, and algorithmic aspects.
In particular, we will mention a number of unsolved problems and future directions in related areas on hypercubes. | 10/4/2019 7:30:00 PM | 10/4/2019 8:30:00 PM | False | |
| Sebastian Roch, University of Wisconsin | Sebastian Roch, University of Wisconsin | GOR 104 | <br>
Title:
From genomes to evolutionary trees and beyond <br><br>
Abstract: The reconstruction of the Tree of Life is a classical problem in evolutionary biology that has benefited from numerous branches of mathematics, including probability, information theory, combinatorics, and geometry. Modern DNA sequencing technologies are producing a deluge of new genetic data -- transforming how we view the Tree of Life and how it is reconstructed. I will survey recent progress on some statistical questions that arise in this context. <br><br>
Refreshments and reception in 536 Ewing Hall • 4:30pm | 5/10/2019 7:30:00 PM | 5/10/2019 8:30:00 PM | False | |
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