From malkiewich at math.binghamton.edu Tue Oct 3 08:14:39 2023 From: malkiewich at math.binghamton.edu (Cary Malkiewich) Date: Tue, 3 Oct 2023 08:14:39 -0400 Subject: [Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Cary Malkiewich Message-ID: Hi everyone, OK, let's try this again! This week I'll be speaking in our geometry and topology seminar on scissors congruence, title and abstract below. This will be an in person talk, on Thursday at 2:50pm in WH 100E. We will also have a lunch social, meet at 12pm just outside WH100E. See you there! Best, Cary %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% *Title:* Higher scissors congruence *Abstract:* Hilbert's Third Problem asks for sufficient conditions that determine when two polyhedra in three-dimensional Euclidean space are scissors congruent. Classically, the attempts to solve this problem (in this and other geometries) lead into group homology and algebraic K-theory, in a somewhat ad-hoc way. In the last decade, Zakharevich has shown that the presence of K-theory here is not ad-hoc, but is integral to the definition of scissors congruence itself. This leads to a natural notion of higher scissors congruence groups, in which the 0th group is the classical one that determines the answer to Hilbert's Third Problem. In this talk, I'll describe a surprising recent result that these higher groups arise from a Thom spectrum. Its base space is the homotopy orbit space of a Tits complex, and the vector bundle is the negative tangent bundle of the underlying geometry. Using this result, we can explicitly compute the higher scissors congruence groups for the one-dimensional geometries, and give exact sequences that express them for the two-dimensional geometries. Much of this is joint work with Anna-Marie Bohmann, Teena Gerhardt, Mona Merling, and Inna Zakharevich. -------------- next part -------------- An HTML attachment was scrubbed... URL: From malkiewich at math.binghamton.edu Thu Oct 5 14:46:05 2023 From: malkiewich at math.binghamton.edu (Cary Malkiewich) Date: Thu, 5 Oct 2023 14:46:05 -0400 Subject: [Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Cary Malkiewich In-Reply-To: References: Message-ID: A quick reminder about topology seminar today (in 5 minutes), sorry for not sending it out this morning! Cary On Tue, Oct 3, 2023 at 8:14?AM Cary Malkiewich < malkiewich at math.binghamton.edu> wrote: > Hi everyone, > > OK, let's try this again! This week I'll be speaking in our geometry and > topology seminar on scissors congruence, title and abstract below. This > will be an in person talk, on Thursday at 2:50pm in WH 100E. > > We will also have a lunch social, meet at 12pm just outside WH100E. See > you there! > > Best, > Cary > > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% > *Title:* Higher scissors congruence > *Abstract:* Hilbert's Third Problem asks for sufficient conditions that > determine when two polyhedra in three-dimensional Euclidean space are > scissors congruent. Classically, the attempts to solve this problem (in > this and other geometries) lead into group homology and algebraic K-theory, > in a somewhat ad-hoc way. In the last decade, Zakharevich has shown that > the presence of K-theory here is not ad-hoc, but is integral to the > definition of scissors congruence itself. This leads to a natural notion of > higher scissors congruence groups, in which the 0th group is the classical > one that determines the answer to Hilbert's Third Problem. > > In this talk, I'll describe a surprising recent result that these higher > groups arise from a Thom spectrum. Its base space is the homotopy orbit > space of a Tits complex, and the vector bundle is the negative tangent > bundle of the underlying geometry. Using this result, we can explicitly > compute the higher scissors congruence groups for the one-dimensional > geometries, and give exact sequences that express them for the > two-dimensional geometries. Much of this is joint work with Anna-Marie > Bohmann, Teena Gerhardt, Mona Merling, and Inna Zakharevich. > > -------------- next part -------------- An HTML attachment was scrubbed... URL: From malkiewich at math.binghamton.edu Tue Oct 10 16:54:06 2023 From: malkiewich at math.binghamton.edu (Cary Malkiewich) Date: Tue, 10 Oct 2023 16:54:06 -0400 Subject: [Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Jenya Sapir Message-ID: Hi everyone, This week we are pleased to have our very own Jenya Sapir speaking about geodesic current, title and abstract below. This will be an in person talk, on Thursday at 2:50pm in WH 100E. We will also have a lunch social, meet at 12pm just outside WH100E. See you there! Best, Cary %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% *Title:* Geometry of geodesic currents *Abstract:* The space of projective, filling currents PFC(S) contains many structures relating to a closed, genus g surface S. For example, it contains the set of all closed curves on S, as well as an embedded copy of Teichmuller space, and many other spaces of metrics on S. We will discuss a structure theorem that compares each filling current with a suitably chosen point in Teichmuller space. We will then use this structure theorem to explore the geometry of PFC(S) under an extension of the Thurston metric. -------------- next part -------------- An HTML attachment was scrubbed... URL: From malkiewich at math.binghamton.edu Thu Oct 12 11:51:41 2023 From: malkiewich at math.binghamton.edu (Cary Malkiewich) Date: Thu, 12 Oct 2023 11:51:41 -0400 Subject: [Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Jenya Sapir In-Reply-To: References: Message-ID: Hi everyone, A quick reminder about Jenya's talk today at 2:50pm, and topology lunch at noon. See you there! Cary On Tue, Oct 10, 2023 at 4:54?PM Cary Malkiewich < malkiewich at math.binghamton.edu> wrote: > Hi everyone, > > This week we are pleased to have our very own Jenya Sapir speaking about > geodesic current, title and abstract below. This will be an in person talk, > on Thursday at 2:50pm in WH 100E. > > We will also have a lunch social, meet at 12pm just outside WH100E. See > you there! > > Best, > Cary > > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% > *Title:* Geometry of geodesic currents > *Abstract:* The space of projective, filling currents PFC(S) contains > many structures relating to a closed, genus g surface S. For example, it > contains the set of all closed curves on S, as well as an embedded copy of > Teichmuller space, and many other spaces of metrics on S. We will discuss a > structure theorem that compares each filling current with a suitably chosen > point in Teichmuller space. We will then use this structure theorem to > explore the geometry of PFC(S) under an extension of the Thurston metric. > -------------- next part -------------- An HTML attachment was scrubbed... URL: From malkiewich at math.binghamton.edu Mon Oct 23 10:44:21 2023 From: malkiewich at math.binghamton.edu (Cary Malkiewich) Date: Mon, 23 Oct 2023 10:44:21 -0400 Subject: [Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Brenda Johnson Message-ID: Hi everyone, This week we are pleased to have Brenda Johnson (Union College) speaking about functor calculus, title and abstract below. This will be an in person talk, on Thursday at 2:50pm in WH 100E. Our speaker will not be on campus in time for lunch, but we will still do our usual gathering at 12pm just outside WH100E. See you there! Best, Cary %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% *Title:* What is (functor) calculus? *Abstract:* Goodwillie?s calculus of homotopy functors is an important topological tool that has been used to shed light on and make connections between fundamental structures in homotopy theory and K-theory. It has also inspired the creation of new types of functor calculi to tackle problems in algebra and topology. In this talk, I will begin by describing Goodwillie?s calculus and some of these other types of functor calculi. I will then address more general questions about what the essential features of something called ?functor calculus? should be and the types of conditions and ingredients that are sufficient for creating new functor calculi. -------------- next part -------------- An HTML attachment was scrubbed... URL: From malkiewich at math.binghamton.edu Thu Oct 26 09:13:00 2023 From: malkiewich at math.binghamton.edu (Cary Malkiewich) Date: Thu, 26 Oct 2023 09:13:00 -0400 Subject: [Binghamton Geometry Topology Seminar] Fwd: Geometry and Topology seminar: Brenda Johnson In-Reply-To: References: Message-ID: Hi everyone, A quick reminder about Brenda's talk today! The topology caucus will also meet immediately after to discuss courses for 2024-2025. See you there! Cary ---------- Forwarded message --------- From: Cary Malkiewich Date: Mon, Oct 23, 2023 at 10:44?AM Subject: Geometry and Topology seminar: Brenda Johnson To: , Math Dept Binghamton < math-dept at math.binghamton.edu>, Johnson, Brenda Hi everyone, This week we are pleased to have Brenda Johnson (Union College) speaking about functor calculus, title and abstract below. This will be an in person talk, on Thursday at 2:50pm in WH 100E. Our speaker will not be on campus in time for lunch, but we will still do our usual gathering at 12pm just outside WH100E. See you there! Best, Cary %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% *Title:* What is (functor) calculus? *Abstract:* Goodwillie?s calculus of homotopy functors is an important topological tool that has been used to shed light on and make connections between fundamental structures in homotopy theory and K-theory. It has also inspired the creation of new types of functor calculi to tackle problems in algebra and topology. In this talk, I will begin by describing Goodwillie?s calculus and some of these other types of functor calculi. I will then address more general questions about what the essential features of something called ?functor calculus? should be and the types of conditions and ingredients that are sufficient for creating new functor calculi. -------------- next part -------------- An HTML attachment was scrubbed... URL: From malkiewich at math.binghamton.edu Mon Oct 30 09:15:51 2023 From: malkiewich at math.binghamton.edu (Cary Malkiewich) Date: Mon, 30 Oct 2023 09:15:51 -0400 Subject: [Binghamton Geometry Topology Seminar] Geometry and Topology seminar: Paul Apisa Message-ID: Hi everyone, This week we are pleased to have Paul Apisa (University of Wisconsin) speaking about orbit closures in moduli space, title and abstract below. This will be an in person talk, on Thursday at 2:50pm in WH 100E. We will also have a lunch social, meet at 12pm just outside WH100E. See you there! Best, Cary ========================================= *Title:* Hurwitz Spaces, Hecke Actions, and Orbit Closures in Moduli Space *Abstract:* The moduli space of Riemann surfaces is a space whose points correspond to the ways to endow a surface with a hyperbolic metric or, equivalently, complex structure. Geodesic flow on moduli space can be used to generate an action of GL(2, R) on its cotangent bundle. While work of Eskin, Mirzakhani, Mohammadi, and Filip implies that GL(2, R) orbit closures are varieties, the question of which ones occur is wide open. Aside from two well-understood constructions (taking loci of branched covers and subloci of rank two orbit closures) there are only 3 known families of orbit closures: the Bouw-Moller curves, the Eskin-McMullen-Mukamel-Wright (EMMW) examples, and 2 sporadic examples. Building on ideas of Delecroix-Rueth-Wright, I will describe work showing that the Bouw-Moller and EMMW examples can be constructed using just the representation theory of finite groups. The main idea is to connect these examples to Hurwitz spaces of G-regular covers of the sphere for an appropriate finite group G. In the end, I will describe a construction that inputs a finite group G and a set of generators satisfying a combinatorial condition and outputs a GL(2, R) orbit closure in moduli space. -------------- next part -------------- An HTML attachment was scrubbed... URL: