Usual meetings: Wednesdays at 4:40pm, WH 309
The Mathematics Graduate Student Seminar seeks to strengthen communication among grad students at Binghamton University, thereby cultivating our community and fostering a friendly environment in which to do mathematics research. We provide a venue for grad student talks on interesting math; we also hope to stimulate discussion around various topics--mathematical and otherwise--relevant to math grad students.
Presentations should be accessible to mathematics grad students, and all are encouraged to contribute a talk!
Email Andrew Velasquez-Berroteran or Tara Koskulitz (math emails velasqua and koskulitz, respectively) to schedule your talk!
For a list of talks from previous semesters, see the link in the top right corner.
Sept. 4 : Organizational Meeting
Sept. 11 : Naftoli Kolodny, The Full L-Theory of the Naturals is Undecidable
Abstract: The Halting problem is famous in mathematics and computer science: There does not exist an algorithm that, given another algorithm as input, can determine whether that input algorithm will halt. Model theory is a branch of mathematics dedicated to studying fundamental mathematical structures. Here, we apply the halting problem to a particularly interesting structure in model theory: The L-Theory of the Naturals. The talk will be based on David Marker's book on Model Theory.
Sept. 18: Benjamin Warren, 19th, 20th, and 21st Century Triangle Geometry
Abstract: Come one, come all, we'll have a blast, we'll have a ball!
We will explore a survey of various topics and results in the 19th, 20th, and 21st century plane geometry of the triangle and quadrilateral. Included will be talks about Clark Kimberling's Encyclopedia of Triangle Centers, various perspectors, Desargues theorem, the radical center theorem, Varignon's theorem, Ceva's theorem, Lester's theorem, Kosnita's theorem, Bottema's theorem, Dao's theorems, Johnson's theorem, Napoleon's theorem, Brianchon's theorem, Barlotti's theorem, Van Aubel's theorem, Newton's theorem, Euler's quadrilateral theorem, the Euler-Chapple theorem, the Gauss-Bodenmiller theorem, Steiner's theorems, Pappus' theorem, Pascal's theorem, Miquel's theorem, Jacobi's theorem, isogonal and isotomic conjugates, the Kiepert Hyperbola, the Van Lamoen circle, the Conway circle, the Nine point circle, the Euler line, the Nagel line, the Simson line, the Droz-Farny line, and much more!
Sept. 25: No Meeting
Oct. 2: No Meeting (Rosh Hashanah/Fall Break)
Oct. 9: No Meeting
Oct. 16: Levi Axelrod, Hyperreal Analysis: How to Rigorously do Calculus where dx is a Number
Abstract: Let's talk about the hyperreal numbers: a number system including infinitesimals and infinite numbers. It turns out there is an extremely intuitive construction of such a system, and that this system makes a lot of calculus ideas more intuitive! In this talk, we'll discuss the construction of the hyperreals, the transfer principle (magic that makes everything work), and the definitions and proofs of some basic calculus concepts using the hyperreals.
Oct. 23: No Meeting (Preparing for BUGCAT!)
Oct. 30: Naftoli Kolodny, Finitely Generated Spaces, Preorders, and Topological Algebra
Abstract: Finite topological spaces are a rich source of basic examples and counterexamples for many conjectures and theorems in topology, but they are generally of limited interest. In this talk, we will define a generalization of finite topological spaces, called Finitely Generated, or Alexandrov spaces. We will prove various properties about them, before finally proving an equivalence between Alexandrov spaces and Preorders on sets. This has natural implications in algebra and order theory, providing a way to study algebraic structures and (pre)ordered sets using their corresponding induced topologies, leading to studies in Topological Algebra.
Nov. 6: Polytope Problem Session
Abstract: In lieu of not having an official speaker, we will be having a discussion on problems regarding polytopes.
Polytopes are a generalization of polyhedra in dimensions higher than 3 and they are convex hulls of finitely many points.
If you are interested in joining us talking about polytopes, feel free to stop by!
Nov. 13: No Meeting
Nov. 20: Han Lim Jang, What Are Buildings in Mathematics?
Abstract: In this talk, I will introduce the definition of buildings with several examples. While there are several definitions about buildings, the one I will talk about is given by Jacques Tits. This version defines a building as a simplicial complex which is a union of Coxeter complexes.
Nov. 27: No Meeting (Thanksgiving Break)
Dec. 4: