Configuration Spaces and Related Topics

Department of Mathematics Education, Kyungpook National University, Daegu, Korea

August 4–9, 2024

Invited Speakers

  • Nir Gadish (University of Michigan)
  • Sangjin Lee (Konkuk University)
  • Sangrok Oh (University of the Basque Country)
  • Jihoon Park (Kyungpook National University)
  • Eric Ramos (Stevens Institute of Technology)
  • Nicholas Wawrykow (University of Chicago)

Organizers

  • Byung Hee An (Kyungpook National University)
  • Ben Knudsen (Northeastern University)

Local Organizer

  • Jihoon Park (Kyungpook National University)

Participants

  1. Byung Hee An (Kyungpook National University)
  2. Sunghyun Byun (Kyungpook National University)
  3. Seonmi Choi (Kyungpook National University)
  4. Nir Gadish (University of Michigan)
  5. Donghoon Jang (Pusan National University)
  6. Ben Knudsen (Northeastern University)
  7. Joonhyung Kim (Chungnam National University)
  8. Sanghoon Kwak (KIAS)
  9. Junseok Kim (KAIST)
  10. Hyunwoo Lee (Kyungpook National University)
  11. Sangjin Lee (Konkuk University)
  12. SeongWoo Lee (Kyungpook National University)
  13. Sangsoo Lee (Kyungpook National University)
  14. Sangrok Oh (University of the Basque Country)
  15. Semin Oh (Kyungpook National University)
  16. Jihoon Park (Kyungpook National University)
  17. Eric Ramos (Stevens Institute of Technology)
  18. Donggyun Seo (Seoul National University)
  19. Nicholas Wawrykow (University of Chicago)
  20. Seung Yeop Yang (Kyungpook National University)

Venue

Talk Schedule

August 4 (Sun) August 5 (Mon) August 6 (Tue) August 7 (Wed) August 8 (Thu) August 9 (Fri)
09:50 – 10:00 Arrival
and
Registration		 Opening Remark
10:00 – 10:50 Sangjin Lee Jihoon Park Excursion Sangrok Oh Free Discussion
10:50 – 11:10 Break Break
11:10 – 12:00 Sangjin Lee Jihoon Park Sangrok Oh
12:00 – 14:00 Lunch Lunch
14:00 – 14:50 Nicholas Wawrykow Nir Gadish Eric Ramos Free Discussion
14:50 – 15:10 Break Break
15:10 – 16:00 Free Discussion Nicholas Wawrykow Nir Gadish Eric Ramos
16:00 – 16:10 Break Break
16:10 – 17:00 Free Discussion Free Discussion Free Discussion
17:00 – 18:00
18:00 – Workshop Dinner Workshop Dinner Workshop Dinner

* The schedule may vary.

Online Participation

For online participation, please follow the zoom link here.

Title & Abstract

Abstracts

Speaker
Nir Gadish (University of Michigan)
Title
Compactified configurations of points on wedges of spheres as polynomial functors
Abstract
Configurations on wedges of spheres stand at a surprising meeting point of seemingly unrelated topics: unstable cohomology of mapping class groups, representations of Out(F_n), high-dimensional knot theory, and higher Hochschild homology. Specifically, applications require the compactly supported cohomology of these configuration spaces, along with the action of maps between wedges of spheres. After explaining how these configuration spaces arise in motivating applications, we will discuss the algebraic structures that assist us in computations: the cohomology turns out to have a uniform presentation, independent of the number of spheres and their dimensions, formalized using the notion of polynomial functors.
Speaker
Sangjin Lee (Konkuk University)
Title
Translation lengths of right-angled Artin groups on the extension graphs
Abstract
When a group $G$ acts on a metric space $(X,d)$ by isometries, the \emph{translation length} of an element $g$ of $G$ is defined by $$ \tau(g)=\lim_{n\to\infty}\frac{d(x,g^nx)}{n}, $$ where $x\in X$. For the action of a right-angled Artin group on the extension graph, it is known that the minimal nonzero translation length is at most 2 provided that the defining graph has diameter at least 3. In the talk, we show that the same result holds for any defining graph. This is done by exploring some graph theoretic properties of biconnected graphs, i.e. connected graphs whose complement is also connected. This is a joint work with Eon-Kyung Lee.
Speaker
Sangrok Oh (University of the Basque Country)
Title
Large scale geometry of graph braid groups
Abstract
The intersection complex of the universal cover of a special square complex is a quasi-isometry invariant which encodes the information that quasiflats are preserved by a quasi-isometry up to finite Hausdorff distance. In this talk, we will use the intersection complex to classify a certain class of graph 2-braid groups, which are the fundamental groups of special square complexes, up to quasi-isometries. Moreover, we will see when such a graph 2-braid group is quasi-isometric to a right-angled Artin group. This is a joint work with Byunghee An.
Speaker
Jihoon Park (Kyungpook National University)
Title
Slice stabilizer property of combinatorial HHG and embeddability of RAAGs into CHHG
Abstract
Hierarchically Hyperbolic Space(HHS) is a large-scale geometric structure which utilize geometry of both mapping class groups of surfaces and CAT(0) cube complex. One main interest about HHS theory is to extend geometric, algebraic results of hyperbolic groups and MCG to the groups acting on HHS. In this talk, we focus on groups acting on a combinatorial HHS and its slice stabilizer property, and we will show that given a collection $\{U_i\mid diam(CU_i) = \infty\}$ of unbounded domains of CHHS, there exists a collection of elements $\{g_i \in stab_G(FU_i)\}$ which generates a right-angled Artin subgroup of CHHG.
Speaker
Eric Ramos (Stevens Institute of Technology)
Title
The ever-growing kinds of stability in graph configuration spaces
Abstract
Dating back to the works of mathematicians such as Arnold, McDuff, and Segal, it has been known that the unordered configuration spaces of higher dimensional manifolds display homological stability in each degree once enough points have been added. More recently, seminal work of Church, Ellenberg, and Farb, expanded these ideas to the ordered case using the machinery of representation stability. If we instead look at graphs, it is notable that the homology groups of (un)ordered configuration spaces usually exhibit neither stability nor representation stability. Work over the last 5-or-so years from several authors has illustrated that there are still universal behaviors manifesting in these spaces, but they are tied more to the structural graph theory of the underlying graph. In this talk I will survey a number of these results, both proven and conjectural.
Speaker
Nicholas Wawrykow (University of Chicago)
Talk 1
Disk configuration spaces
Abstract
Disk configuration spaces are a natural generalization of point configuration spaces in which the geometry of the underlying space comes into play. In this talk, we will look at several disk configuration spaces and discuss how their topology relates to that of point configuration spaces. We will demonstrate how many of these disk configuration spaces can be viewed as cellular complexes with nice combinatorial properties. This will allow us to describe their homology in detail.
Talk 2
Disk configuration spaces and topological complexity
Abstract
Given a space X, how hard is it to design an algorithm that gives a path in X that varies continuously with the choice of start and end points. The difficulty of this motion planning problem can be encapsulated in a homotopy invariant called topological complexity. In this talk, we focus on $conf(n, w)$, the ordered configuration space of n open unit-diameter disks in the infinite strip of width w, and we calculate its topological complexity by finding disjoint tori. After that we will discuss several open problems about disk configuration spaces.

Registration

For registration, please fill up the registration form below.

https://docs.google.com/forms/d/1KZQUhYhJnQb_VKZjX-ZRhX2pkyvMQB8q_6pL3vc4R9w/

Accommodation Suggestion

Excursion

The conference excursion is on Wednesday, August 7, and we will travel near the Nakdonggang river. We will meet at Dongdaegu Station at 10am on Wednesday, and the excursion will end at 6pm. Please refer to the Daegu City Tour Website (Korean) and the tour leaflet.

Getting to KNU

From Incheon International Airport

There are two popular options getting to Daegu from Incheon International Airport.

AREX (Airport Railroad Expresses) + KTX
  1. AREX from Incheon International Airport to Seoul Station departs very often and takes 67min(all-stop commuter train, KRW 5,050, non-reserved seat) or 57min(non-stop train, KRW 11,000, reserved seat). Please refer to the AREX Website for reservation of non-stop trains.
  2. KTX from Seoul Station to Dongdaegu Station departs more than 100times per day and takes about two and half hours. The fare is KRW 43,500. It is usually very crowded. We recommend booking tickets in advance. The ticket reservation website is here.
Airport Limousine Bus

The Airport Limousine Bus to Dongdaegu Bus Terminal operates 30times and takes about 4hours. The fare is KRW 41,500(daytime) or KRW 45,700(midnight, from 10:20pm). Please refer to the BUSTAGO website.

From Gimhae International Airport

We highly recommend to take the Airport Limousine Bus to Dongdaegu Bus Terminal. It operates 26times from 7am to 10:30pm, and takes about an hour and a half. The fare is KRW 11,100 (daytime) or KRW 12,200 (midnight, from 10pm). Please refer to the BUSTAGO website.

From Daegu International Airport, Dongdaegu Station, or Dongdaegu Bus Terminal to KNU

Daegu International Airport, Dongdaegu Station, and Dongdaegu Bus Terminal are very close to the KNU. You can take a taxi. It takes about 15min, and the fare is about KRW 7,000. FYI, Dongdaegu Bus Terminal and Dongdaegu Station are next to each other. Please refer to the KNU Website.

Dining Suggestion

Category Restaurant Speciality Distance from Campus Map link
Korean Hanggi galbi 한끼갈비 Korean dish 15 min walk 7-1, Daehak-ro 17gil, Buk-gu
Korean Hyunpoong dalkkalguksu 현풍닭칼국수 Korean noodle 10 min walk 105, Daehak-ro, Buk-gu
Japanese Katsuya 까츠야 Japanese ramen, Pork/beef cutlet 10 min walk 31-1, Daehak-ro 23gil, Buk-gu
Japanese Ginza Ryoko 긴자료코 Japanese ramen, Pork/beef cutlet 10 min walk 99-4, Daehak-ro, Buk-gu
Chinese Pudong 푸둥 Chinese food 15 min walk 29-3, Sangyeok-ro 6gil, Buk-gu

Contact

Samsung STF
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