The Graduate Student Colloquium is geared towards introducing graduate students to different areas of mathematics. Each week a different member of the Graduate Center Mathematics Department faculty will discuss a topic that is accessible to all graduate students. All graduate students without an advisor are required to attend, but even those with an advisor are welcome! Faculty members are strongly discouraged from attending. All meetings of the Graduate Student Colloquium will be held on Mondays from 4:00-4:45 PM in the Room 6495, unless otherwise stated.Organizers: Jacob Russell: jrussellmadonia@gradcenter.cuny.edu Qian Chen: qchen@gradcenter.cuny.edu Joe DiCapua: jdicapua@gradcenter.cuny.edu Professor Alexander Gamburd: agamburd@gmail.com Fall 2017 ScheduleSeptember 18th, 2017 Russell Miller qcpages.qc.cuny.edu/~rmiller/ Title: Classification of Algebraic Fields Abstract: Every field has a smallest subfield: either a copy of the rational numbers, or a copy of the p-element field, depending on whether the characteristic is 0 or a positive prime p. A field is algebraic if it is an algebraic extension of this subfield, with every element of the field satisfying some polynomial over the subfield. We will focus here on characteristic 0. The first question to be discussed is what counts as a classification. Normally one would like to be able to give a list of all the isomorphism types of such fields, in such a way that, for each field, we can find its place on the list, and for each place on the list, we can determine the corresponding field. Saying "we can find" and "we can determine" suggest questions of effectiveness: we would like to be able to compute the bijection between fields and places on the list. Therefore, computability theory will enter into the talk. Surprisingly, so will topology, along with (less surprisingly) a bit of algebra and field theory, and we will explain how all these areas intersect and yield our classification. September 25th, 2017 Thomas Tradler Title: Operads, Associahedra, and Infinity-AlgebrasAbstract: I will introduce operads, which are gadgets that describe the underlying algebraic structure of some algebraic notion, such as, for example, the notion of an "associative algebra." Operads are very well suited to study problems up to homotopy. I will show this for the case of homotopy associative algebras and show its connection to the combinatorics of associahedra. Although these ideas were studied and well-understood in the 1960s, 1970s and 1990s, similar techniques can be used to analyze other algebraic notions, that do not precisely fit into this language. I will show this for the notion of an "associative algebra with a co-inner product," which comes up, for example, in the study of string topology. October 2nd, 2017 Luis Fernandez October 9th, 2017 No SeminarOctober 16th, 2017 Christian WolfOctober 23rd, 2017 Andrew Douglas October 30th, 2017 Joseph MaherNovember 6th, 2017 Olga KharlampovichNovember 13th, 2017 TBANovember 20th, 2017 TBA |

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