Scotty Tilton

Research Interests

I'm interested in finding ways in which $\mathsf{Pin}(2)$-equivariant homotopy theory can answer questions about exotic phenomena in 4-manifolds using families Bauer-Furuta invariants as described in Kronheimer-Mrowka, Baraglia-Konno, and Lin. This is interesting to me because this is in the intersection of (equivariant) stable homotopy theory and low-dimensional topology.${\quad}^\ast$

I also have a whole lot of fun thinking about shapes, and I like arguments in combinatorics because when things come together there I whoop for joy. So if you like thinking about shapes and counting things, then you can count (the shape of) me in to whatever you're trying to think about! (For example see the pretty shapes in the Grassmannians paper (and counting things!) and the pretty shapes in the Transfer systems paper (and counting things!)).

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Research Paper(s)

• Transfer systems for rank two elementary Abelian groups: characteristic functions and matchstick games
  (with Linus Bao, Christy Hazel, Tia Karkos, Alice Kessler, Austin Nicolas, Kyle Ormsby, Jeremie Park, Cait Schleff Oct 2023) On the arXiv.
• The cohomology of real Grassmannians via Schubert Stratifications
  (with Eric Berry Nov 2020) On the arXiv.

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Seminars I'm Attending

• UCSD Topology Seminar
• UCSD Grads-Food For Thought
• eCHT Research Seminar
• GT GAPS

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Talks I've Given

Date - Location	Title	Extra
Apr 2024 - UCSD Topology HLSX Seminar	Sections 1.1-1.3	No Extra
Feb 2024 - UCSD Topology arXiv Seminar	The homology of moduli spaces of 4-manifolds can be infinitely generated	Extra Slides Link to paper
Nov 2023 - UCSD Topology Seminar	MMF	Extra Slides
Nov 2023 - UCLA Algebraic Topology Seminar	Dehn it! Distinguishing diffeomorphisms with Equivariant Bauer-Furuta Invariants	Extra Slides
Oct 2023 - UCSD Topology Seminar (arXiv series)	A Note on Surfaces in $\mathbb{CP}^2$ and $\mathbb{CP}^2\#\mathbb{CP}^2$	No Extra
June/July 2023 - eCHT REU	Operads 101	Extra 101A Slides 101$N_\infty$
May 2023 UCSD Topology Seminar	Factorization Homology 101	Extra Slides Hiro's Book Ayala-Francis' F.H. Primer
4/23 Taubes Secret Seminar	A Note on A Note on Surfaces in $\mathbb{CP}^2$ and $\mathbb{CP}^2\#\mathbb{CP}^2$	Extra Slides 1 Slides 2 arXiv Paper
1/23 UCSD Topology Seminar	Pin(2)-Bauer-Furta Invariants	Extra Slides
10/22 - UCSD Topology Seminar	Equivariant Transfer maps, the Wirthmuller isomorphism, and dualities.	No Extras
4/22 - UCSD ZFT Seminar	Four Four Manifolds For Food For Thought	Extra Slides
1/22 - UCSD Topology Seminar	Morava's Orbit Picture and Stabilizer Groups	Extra Slides Ref: The Orange Book
1/22 - UCSD Topology Seminar	MU-Theory and Formal Group Laws	Extra Slides Ref: The Orange Book
11/2021 - UCSD Topology Seminar	Introduction to Spectra I	Extra Slides
4/21 - Augustana University	Stratified Spaces and Grassmannians	Extra Video Slides
2/21 - UCSD ZFT Seminar	Stay at (co)home: Links, Blowups, and Grass, man.	Extra Abstract Prezi Slides Video Certificate

The Extra dropdown menus are broken on Desktop. I'm working on fixing these, but until then, if you make your browser window have the width of a phone, you should be able to see everything okay.

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Conferences/Workshops I've Attended

Date	Title	Participation
August 2023	Symplectic Paradise	Attendee
July 2023	Gauge Theory and Topology, Kronheimer's 60th Birthday	Attendee
March 2023	Homotopy 2023, Goerssfest	Attendee
November 2022	Floer Homotopical Methods in Low Dimensional and Symplectic Topology	Attendee
September 2022	Introductory Workshop: Floer Homotopy Theory	Attendee
February 2020	Higher Categories and Categorification	Attendee
February 2020	Connections for Women: Higher Categories and Categorification	Attendee
May 2019	Moab Topology Conference	Attendee
April 2019	National Conference for Undergraduate Research	Poster Presenter
January 2019	Joint Math Meetings	Poster Presenter
May 2018	Arches Topology Conference	Attendee

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${\quad}^\ast$ Scotty, I'll be honest with you, that doesn't sound interesting to me in terms of the real world.
-- A good friend

Well, here's how I think of it. Mathematicians are trying to stay a few steps ahead of the physicists. If a physicist has a problem, they might come up to a mathematician and ask if the mathematician knows anything about the problem. It'd be nice if the mathematicians had solved it ages ago, so the physicist can get back to work with their real-world problem. Physicists, oftentimes, deal with manifolds.

Mathematicians spend a lot of time classifying things. Algebraists classified all finite groups. Topologists classified 0-manifolds, 1-manifolds, 2-manifolds, $\geq$5-manifolds, 4-manifolds, and 3-manifolds in the topological category. In the smooth category, most of those are also taken care of, but the 4th dimension is giving mathematicians some trouble. There are a lot of exotic smooth structures, and no one has made sense of when and where to expect them, in general (there has been some progress, but no one claims to know it all). This $\mathsf{Pin}(2)$-equivariant method has proven itself by detecting some exotic smooth structures. I want to keep searching with this to see if I can help other mathematicians in finding some patterns to the smooth structures so we can see if there is a way to classify them.