Hi Everyone,

Sorry for the late email on this. Things were a little out of whack with the room scheduling. So we have a different time and place for the seminar this week.

Today we will hold the seminar at 2:30 in MSCS 101.

Topology Seminar Title: Embeddability in R 3 is NP-hard Speaker: Eric Sedgwick, Depaul University Date: Oct 4, 2022 Time: 2:30 PM Room: MSCS 101

Abstract: We prove that the problem of deciding whether a 2–or 3–dimensional simplicial complex embeds into R 3 is NP-hard. This stands in contrast with the lower dimensional cases which can be solved in linear time, and a variety of computational problems in R 3 like unknot or 3–sphere recognition which are in NP∩co-NP (assuming the generalized Riemann hypothesis). Our reduction encodes a satisfiability instance into the embeddability problem of a 3–manifold with boundary tori, and relies extensively on techniques from lowdimensional topology, most importantly Dehn fillings on link complements. This is joint work with Arnaud de Mesmay (CNRS, GIPSA-Lab, France), Yo’av Rieck (University of Arkansas, USA) and Martin Tancer (Charles University, Czech Republic).

Best, Neil

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Neil R. Hoffman Assistant Professor Department of Mathematics 523 Math Science Building Oklahoma State University Stillwater, OK 74078-1058 405-744-7791 http://math.okstate.edu/people/nhoffman