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Title: Ehrhart polynomials with negative coefficients



Abstract: The Ehrhart polynomials of integral convex polytopes count integer points under dilations of the polytopes. In this talk, I will discuss the possible sign patterns of the coefficients of Ehrhart polynomials of integral convex polytopes. While the leading terms, the second leading terms and the constant of Ehrhart polynomials are always positive, the other terms aren't necessarily positive.  In fact, some examples of Ehrhart polynomials with negative coefficients were known before. For arbitrary dimension, I will describe a construction of Ehrhart polynomials with negative coefficients. 

Wesley Hough will present the documentary "In the Footsteps of Newton", which he worked on while he was a undergraduate at Hanover College.  For more details on the documentary visit the following link.  Come and hangout with other mathematically minded students at the first math club meeting of the semester. There will be pizza.

Title: The Waldschmidt constant

Abstract:  A (projective) variety V is a set of common zeros of the polynomials in an ideal I that is generated by homogenous polynomials. Given the generators of the ideal I,  one would like to know the minimum degree of a polynomial F such that each point of V is a root of f of a given multiplicity, say k. As this is often a difficult problem one studies first the corresponding question for large k. This leads to the Waldschmidt constant, which gives an asymptotic answer to the problem.

If I is a an ideal that is generated by squarefree monomials, then the Waldschmidt constant can be expressed as the optimal solution to a linear program or as a fractional chromatic number. This leads to the new bounds and computations of the Waldschmidt constant.

No prior knowledge of monomial ideals or graph theory is assumed. All concepts will be explained in the talk. 

Join SAB and Underground Perspective for a night of dancing, mingling and fun at the SAB Underground Formal on Friday, Feb. 19 from 8 to 11 p.m. in the Commonwealth Stadium Mezzanine Level. This is a formal event where diversity is welcomed and a dress code will be in place. Pull out your best dresses, slacks, ties and jackets; no jeans allowed and come create a night to remember with the people you won’t forget!

As per the University of Kentucky Dance Policy, guests may be admitted by a University of Kentucky student and must be able to document that they are eighteen (18) years of age or older. University of Kentucky students will be held accountable for the behavior of their registered guest(s). A guest list will be maintained at the entrance. UK students will swipe their UK IDs on OrgSync. Their will be a list of non-UK student guests and the student they are accompanying. Attendees must bring UK IDs to the event and if they are a guest, a form of ID that documents their age.