The Graduate Student Seminar is put on by the Mathematics Graduate Student Association . The GSS meets approximately every other Monday.

For the Fall 2015 semester, the GSS meets at 4:00pm in Hayes-Healy 129.

To volunteer to give a talk, or for anything else regarding the seminar, contact PJ Jedlovec.

Date | Speaker | Title |
---|---|---|

Monday, September 7 |
Gabor Szekelyhidi |
Min-max Methods in Geometry |

Monday, September 14 |
Alexander Diaz |
Peak Sets of Classical Coxeter Groups |

Monday, September 28 | Jeremy Mann |
Differential Cohomology |

Monday, October 12 | Alan Liddell |
A hybrid symbolic-numeric approach to exceptional sets of generically zero-dimensional systems |

Monday, October 26 | Eric Wawerczyk |
Congruences of Modular Cusp Forms |

Monday, November 9 | Gabriela Clemente |
Toric manifolds and polytopes |

Monday, November 23 | Michael Perlman |
Minimal Free Resolutions and Hilbert's Syzygy Theorem |

Monday, December 7 | Whitney Liske | |

Date | Speaker | Title |
---|---|---|

Monday, January 18 | Eric Wawerczyk | |

Monday, February 8 | Jeff Madsen | |

Monday, February 15 | Xiaoxiao Li | |

Monday, February 29 | Luis Saumell | |

Monday, March 14 | Xiaoxiao Li | |

Monday, April 4 | Panel on Job Applications | |

Monday, April 11 | Jeremy Mann | |

Monday, April 18 | JD Quigley |

**Speaker**- Gabor Szekelyhidi
**Title**- Min-max Methods in Geometry
**Abstract**- Min-max methods have been used recently to solve several long-standing problems in differential geometry by Fernando Coda Marques and Andre Neves. I will explain the basic idea of the method and I will give a sketch of some of these applications.

**Speaker**- Alexander Diaz
**Title**- Peak Sets of Classical Coxeter Groups
**Abstract**- Given a permutation (or more generally a signed permutation) we can "graph" it and study its "peaks." The combinatorial study of peaks of permutations is a topic that has caught the attention of mathematicians in the past 20 years. For example, it has been shown that the set of sums of permutations with a given peak set is a subalgebra of the group algebra. Extending the notion of peaks to signed permutations, we can generalize some of the results for usual permutations, while some others do not admit a generalization. In this talk I will survey some of the most relevant and beautiful results in this area, including some of my work in collaboration with Jose Pastrana and many others.

**Speaker**- Jeremy Mann
**Title**- Differential Cohomology
**Abstract** A differential cohomology theory produces invariants of manifolds. Like a generalized cohomology theory, these invariants are in some sense “locally determined,” and give global measurements of shape. However, unlike a “regular” cohomology theory, a differential cohomology theory is not homotopy invariant. Thus, these theories can “see” more refined geometric properties of manifolds, such as the curvature of a connection. In this talk, I will present some of the basics aspects of differential cohomology theories, their applications to physics, and their modern formulation

**Speaker**- Alan Liddell
**Title**- A hybrid symbolic-numeric approach to exceptional sets of generically zero-dimensional systems
**Abstract**- Exceptional sets of a parameterized polynomial system are the sets in parameter space where the fiber has higher dimension than at a generic point. Such sets are arise in kinematics, for example, in designing mechanisms which move when the generic case is rigid. In 2008, Sommese
- and Wampler showed that one can use fiber products of bounded order to compute exceptional sets since they become irreducible components of larger systems. We propose an alternative approach using rank constraints on Macaulay matrices. This hybrid symbolic-numerical
- approach first symbolically constructs the appropriate matrices and then uses numerical algebraic geometry to solve the rank-constraint problem. We demonstrate the method on several examples, including exceptional RR dyads, lines on surfaces in C^3, and exceptional planar pentads.

**Speaker**- Eric Wawerczyk
**Title**- Congruences of Modular Cusp Forms
**Abstract**- Sequences of numbers {a_n} arise everywhere. We can study properties of a sequence using different functions: Arithmetic functions, Generating functions, and L-functions. If this sequence of numbers is "modular" then we can say a lot about it. Our specimen is the Ramanujan Tau function \tau(n) which will be our prime example of a ``normalized eigen modular cusp form". We will discuss the duality of weight k modular forms with the weight k Hecke algebra to motivate the key functionalities of a "Hida Family" and their relationship to congruences of modular forms.

**Speaker**- Gabriela Clemente
**Title**- Toric manifolds and polytopes
**Abstract**- We talk about the correspondence between symplectic toric manifolds and Delzant polytopes.

**Speaker**- Michael Perlman
**Title**- Minimal Free Resolutions and Hilbert's Syzygy Theorem
**Abstract**- The idea to associate a free resolution to a finitely generated module was introduced by Hilbert in the late nineteenth century. Minimal free resolutions are invariants of modules that encode algebraic and geometric information. This talk in meant to be an introduction to the theory of minimal resolutions through the computation of several examples. We will prove the Hilbert Syzygy Theorem and provide a geometric application.

**Speaker**- Whitney Liske
**Title****Abstract**

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