July 31 to August 10, 2013

University of Minnesota, Twin Cities

**Organizers:** Selman
Akbulut (Michigan State University), Anar Akhmedov (University of Minnesota),
Weimin Chen (University of Massachusetts, Amherst), Cagri Karakurt (University
of Texas, Austin), Tian-Jun Li (University of Minnesota).

Thanks to the generous support of the National Science Foundation, funds are
available for partial support of participant expenses, such as lodging and
meals. The applicants are kindly asked to seek for travel support from their
home institutions. To apply for funding, you must register by
Friday, April 12, 2013 , but early applications are strongly encouraged
since there are a limited number of rooms available. Students, recent Ph.D.'s,
women, and members of underrepresented minorities are particularly encouraged to
apply. Applicants are requested to register (see the registration form below),
send a CV, and have one brief reference letter sent to Cagri Karakurt at
karakurt@math.utexas.edu. The reference letter is optional for people with a
Ph.D.

***Please note that we are no longer accepting
application*** .

Please check out the information below for transportation options for you to get to the campus/dorm/hotel from the airport.

You can find the transit information in the IMA website .

1. The cheapest way to get to the Math Department or your hotel is by Light Rail. The fair is $1.75 except during peak periods when it is $2.25. It can be faster than taxi, depending on the traffic. Here are directions: take Light Rail to the Metrodome station, and then take bus #16 or #50. For more detailed information, please check the following link: Bus and Light Rail - MSP Airport .

2. There is also a shuttle service ($16)

For more detailed information, please check the following link: Super Shuttle - MSP Airport .

3. By Taxi (about $40 to $45). For more detailed information, please check the following link: Taxi - MSP Airport .

Here is a map showing both the Math dept (Vincent Hall) and Mech E Dept.

Map .

- Selman Akbulut (Michigan State)
- Anar Akhmedov (University of Minnesota)
- Weimin Chen (University of Massachusetts, Amherst)
- Yi-Jen Lee (The Chinese University of Hong Kong)
- Tian-Jun Li (University of Minnesota)
- Ciprian Manolescu (University of California, Los Angeles)
- Chris Wendl (University College London)

**Abstract
of mini courses :**

**4-manifolds
via their handlebodies (by Selman Akbulut)**

**Abstract****:**

Handlebody
descriptions of 3 and 4-manifolds will be discussed, and as time permits their
various applications to 4-manifold problems will be given, such as carving,
branch coverings, knot complements, complex surfaces, Stein manifolds, Lefschetz
fibrations, BLF's, corks and plugs. From these techniques various exotic
manifolds will be constructed, such as going from handlebody of logarithmic
transforms to Dolgachev surfaces, and from handlebody of surface bundles over
surfaces to Akhmedov-Park exotic manifolds.

**
Construction of exotic 4-manifolds (by Anar Akhmedov)**

**Abstract****:**

Lecture 1:
Construction of Lefschetz fibrations via Luttinger surgery

Luttinger
surgery is a certain type of Dehn surgery along a Lagrangian torus in a
symplectic 4-manifold. The surgery was introduced by Karl Murad Luttinger in
1995, who used it to study Lagrangian tori in R^4. Luttinger's surgery has been
very effective tool recently for constructing exotic smooth structures on
4-manifolds. In this talk, using Luttinger surgery, I will present a new
constructions of Lefschetz fibration over 2-sphere whose total space has
arbitrary finitely presented group G as the fundamental group (a joint result
with Burak Ozbagci).

Lecture 2: The geography of symplectic 4-manifolds

The symplectic geography problem, originally posed by Robert Gompf, ask
which ordered pairs of nonnegative integeres are realized as (chi(X), c1^2(X))
for some symplectic 4-manifold X. In this lecture we will address the geography
problem of simply-connected spin and non-spin symplectic 4-manifolds with
nonnegative signature or near the Bogomolov-Miyaoka-Yau line c1^2(X) = 9chi(X)
(joint results with B. Doug Park).

**
Group actions on 4-manifolds (by Weimin Chen)**

**Abstract****:**

In this mini-course
we give an introduction to some basic questions and basic techniques in the
study of finite group actions on 4-manifolds, with an emphasis given to
symplectic finite group actions.

Lecture 1: A general introduction to
finite group actions on 4-manifolds, with emphasis on locally linear topological
actions: basic properties, construction, and obstructions to smoothability.

Lecture 2: Symplectic finite group actions. J-holomorphic curves in
4-orbifolds. Orbifold Seiberg-Witten-Taubes theory.

Lecture 3:
Symplectic actions on CP^2 and K3 surfaces. Some open problems.

**
Elements of HM and ECH (by Yi-Jen Lee)**

**Abstract****:**

I will go over
some background of Seiberg-Witten-Floer homology and ECH (in a generalized
sense), their relations, and if time permits, some computations.

**
The Kodaira dimension of symplectic 4-manifolds (by Tian-Jun Li)**

**Abstract****:**

Lecture 1. Kodaira
dimension for low dimensional manifolds

Lecture 2. Symplectic
4-manifolds with non-positive Kodaira dimension

**
The triangulation conjecture (by Ciprian Manolescu)**

**Abstract****:**

First lecture: The
Seiberg-Witten equations in 3 dimensions

I will review the
Kronheimer-Mrowka construction of monopole Floer homology for 3-manifolds, with
particular emphasis on the Froyshov invariant. I will also discuss the Pin(2)
symmetry that appears in the presence of a spin structure, and some notions of
Pin(2)-equivariant topology.

Second lecture: Finite dimensional
approximation and the Floer spectrum

I will present an alternate
construction of S^1-equivariant Seiberg-Witten Floer homology, based on finite
dimensional approximation and Conley index theory. The construction yields
something more, an S^1-equivariant Floer spectrum. When we have a spin
structure, everything can be tweaked to take into account the
Pin(2)-equivariance of the equations.

Third lecture (conference talk):
The triangulation conjecture

We define Pin(2)-equivariant Seiberg-Witten
Floer homology for rational homology 3-spheres equipped with a spin structure.
The analogue of Froyshov'’s correction term in this setting is an integer-valued
invariant of homology cobordism whose mod 2 reduction is the Rokhlin invariant.
As an application, we show that the 3-dimensional homology cobordism group has
no elements of order 2 that have Rokhlin invariant one. By previous work of
Galewski-Stern and Matumoto, this implies the existence of non-triangulable
high-dimensional manifolds.

**
Lefschetz fibrations and symplectic fillings of contact 3-manifolds (by Chris
Wendl)**

**Abstract****:**

Lefschetz fibrations
have played a major role in symplectic topology since the 1990's, when they
appeared in the topological characterization of closed symplectic 4-manifolds
due to Donaldson and Gompf. A short time later, Giroux introduced a
corresponding characterization of contact manifolds in terms of open book
decompositions, which can be understood as the natural structure arising at the
boundary of a Lefschetz fibration over the disk. My goal in this minicourse
will be to explain the relationship between symplectic/contact structures and
these types of topological decompositions, and to sketch some striking
applications that make use of holomorphic curve technology, e.g. the fact that
all weak fillings of planar contact manifolds are blow-ups of Stein fillings (a
joint result with Niederkrueger), and a recent generalization of that result in
joint work with Lisi and Van Horn-Morris. My perspective on this subject is
rather more geometric than topological: instead of following the topologist's
standard approach of understanding Lefschetz fibrations and Stein structures in
terms of handle decompositions, I will explain a version of the "Thurston trick"
that gives existence and uniqueness (up to deformation) of symplectic and Stein
structures on Lefschetz fibrations over arbitrary surfaces with boundary. I
will then sketch some of the holomorphic curve techniques that give results in
the other direction.

Here is an approximate outline of the content of
the lectures:

LECTURE 1: "Basic notions and results"

Definitions
of contact structures and weak/strong/exact/Stein fillings, Lefschetz
fibrations, spinal open books and contact structures, a theorem on fillings of
partially planar spinal open books, examples and applications.

LECTURE
2: "Symplectic geometry from topological decompositions"

Existence/uniqueness of contact structures on spinal open books (generalizing a
result of Thurston-Winkelnkemper), existence/uniqueness of symplectic and Stein
structures on (allowable) Lefschetz fibrations (generalizing results of Thurston
and Gompf).

LECTURE 3: "Topological decompositions from symplectic
geometry"

Stable Hamiltonian structures, holomorphic curves in completed
symplectic fillings, reconstructing a Lefschetz fibration from a planar open
book at the boundary.

**Lecture
notes and slides from the mini-courses :**

Wednesday 7/31 | Thursday 8/1 | Friday 8/2 | Saturday 8/3 | Sunday 8/4 |

9:00-9:30 Registration and Coffee (math department lounge) |
9:00-9:30 Coffee |
9:00-9:30 Coffee |
9:00-9:30 Coffee |
9:00-9:30 Coffee |

9:30-10:30 W. Chen I |
9:30-10:30 W. Chen II |
9:30-10:30 W. Chen III |
9:30-10:30 C. Manolescu II |
9:30-10:30 Y-J. Lee I |

11:00-12:00 T-J. Li I |
11:00-12:00 T-J. Li II |
11:00-12:00 C. Manolescu I |
11:00-12:00 A. Akhmedov II |
11:00-12:00 Y-J. Lee II |

Lunch | Lunch | Lunch | Lunch | Lunch |

2:00-3:00 S. Akbulut I |
2:00-3:00 S. Akbulut II |
2:00-3:00 C. Wendl III |
2:00-5:00 Short talks | |

3:30-4:30 C. Wendl I |
3:30-4:30 C. Wendl II |
3:30-4:30 A. Akhmedov I | ||

5:30 - 6:30 Soccer |
5:30 Dinner (math department lounge) |
5:30 - 6:30 Soccer |

Schedule of the conference: On the weekdays, the lectures will be in the Mech Engineering Department, Room 18. It is right by the Math Department. It is convenient to enter the building from the left most entrance (going down the stairs). On the weekends, the lectures will be in the Math Dept, Room 16. The lecture room 16 is in the basement of the Math Department.

Monday 8/5 | Tuesday 8/6 | Wednesday 8/7 | Thursday 8/8 | Friday 8/9 | Saturday 8/10 |

9:00-9:30 Registration and Coffee |
9:00-9:30 Coffee |
8:30-9:00 Coffee |
9:00-9:30 Coffee |
9:00-9:30 Coffee |
8:30-9:00 Coffee |

9:30-10:30 C. Manolescu |
9:30-10:30 S. Akbulut |
9:00-10:00 A. Stipsicz |
9:30-10:30 M. Ue |
9:30-10:30 M. Furuta |
9:00-10:00 H-J. Kim |

11:00-12:00 R. Gompf |
11:00-12:00 B. Ozbagci |
10:15-11:15 T. Cochran |
11:00-12:00 Y. Ni |
11:00-12:00 Z. Wu |
10:15-11:15 J. Wang |

Lunch | Lunch | 11:30-12:30 C. Karakurt |
Lunch | Lunch | |

1:30-2:30 D. Auckly |
1:30-2:30 I. Baykur |
free afternoon |
1:30-2:30 H. Endo |
1:30-2:30 M. Usher | |

2:45-3:45 W. Zhang |
2:45-3:45 L. Starkston |
2:45-3:45 M. Hamilton |
2:45-3:45 W. Wu | ||

4:15-5:15 F. Arikan |
4:15-5:15 T. Lidman |
4:15-5:15 J. Dorfmeister |
4:15-5:15 M. Pinnsonault |
||

5:30 - 6:30 Soccer |
5:30 Dinner (math department lounge) |
5:30 - 6:30 Soccer |

**Titles
and abstracts of the talks :**

**
Exotic Stein Fillings (by Selman Akbulut) **

**Abstract****:**

I will construct
infinitely many simply connected compact 4-dimensional Stein handlebodies with
second Betti number 2, such that they are all homeomorphic but not diffeomorphic
to each other, furthermore they are Stein fillings of the same contact
3-manifold. I will briefly explain their role in the world of corks and plugs.
This is a joint work with K. Yasui.

**
Lefschetz Fibrations on Compact Stein Manifolds (by Firat Arikan)
**

**Abstract****:**

We prove that up to
diffeomorphism every compact Stein manifold W of dimension 2n+2>4 admits a
Lefschetz fibration over the two-disk with Stein regular fibers, such that the
monodromy of the fibration is a symplectomorphism induced by compositions of
right-handed Dehn twists along embedded Lagrangian n-spheres on the generic
fiber. Moreover, the induced open book supports the induced contact structure on
the boundary of W. This result generalizes the Stein surface case of n=1,
previously proven by Loi-Piergallini and Akbulut-Ozbagci. This is a joint work
with Selman Akbulut.

**
Strict One-stable Equivalence in Four Dimensions (by David Auckly)
**

**Abstract****:**

A well-known
theorem of Wall establishes that two simply-connected, homeomorphic smooth
$4$-manifolds become diffeomorphic after taking the connected sum with enough
copies of $S^2 \times S^2$. We call two manifolds $n$-stable equivalent if they
are diffeomorphic after taking the connected sum with $n$ copies of $S^2 \times
S^2$. It is less well known, but the analog of Wall's result holds for
topologically isotopic smooth $S^2$s in a $4$-manifold and for topologically
isotopic diffeomorphisms. In this talk we will present smooth $S^2$s that are
strictly $1$-stable equivalent, as well as diffeomorphisms that are strictly
$1$-stable equivalent. (Joint with Danny Ruberman, Paul Melvin, and Hee-Jung
Kim)

**
Topological complexity of symplectic 4-manifolds and Stein fillings (by Inanc
Baykur) **

**Abstract****:**

Following the
ground-breaking works of Donaldson and Giroux, Lefschetz pencils and open books
have become central tools in the study of symplectic 4-manifolds and contact
3-manifolds. An open question at the heart of this relationship is whether or
not there exists an a priori bound on the topological complexity of a symplectic
4-manifold, coming from the genus of a compatible Lefschetz pencil on it, and a
similar question inquires if there is such a bound on any Stein filling of a
fixed contact 3-manifold, coming from the genus of a compatible open book. We
will present our solutions to both questions, making heroic use of positive
factorizations in surface mapping class groups of various flavors. This is joint
work with J. Van Horn-Morris

**
Counterexamples to Kauffman's Conjectures on Slice knots (by Tim Cochran)
**

**Abstract****:**

In the 1960's
Levine introduced a program to decide whether or not a knot is a slice knot by
studying curves on any one of its Seifert surfaces. In support of this
philosophy, in 1982 Louis Kauffman conjectured that if a knot in S^3 is a slice
knot then on any Seifert surface for that knot there exists a (homologically
essential) simple closed curve of self-linking zero which is itself a slice
knot, or at least has Arf invariant zero. Since that time, considerable evidence
has been amassed in support of this conjecture. In particular, many invariants
that obstruct a knot from being a slice knot have been explicitly expressed in
terms of invariants of such curves on the Seifert surface. We give
counterexamples to Kauffman's conjecture, that is, we exhibit (smoothly) slice
knots that admit (unique minimal genus) Seifert surfaces on which every
homologically essential simple closed curve of self-linking zero has non-zero
Arf invariant and non-zero signatures. We not only explain the failure of
Levine's philosophy, but also how it can be repaired

**
Symplectic Sums along Spheres: Minimality and Kodaira Dimension (by Josef
Dorfmesiter) **

**Abstract****:**

Symplectic Sums
have provided the symplectic world with a plethora of examples. In the case of
symplectic 4-manifolds, one fundamental question is under what conditions the
sum is minimal, i.e. contains no embedded sphere of self-intersection -1. This
question was answered by Usher for sums along surfaces of positive genus. I
will detail the result in the case of sums along spheres. Moreover, it is
possible to determine the Kodaira dimension of such sums, the positive genus
case is again Usher's result. Of particular interest is the question if and
when such a sum can have Kodaira dimension 0 and how such examples relate to
known symplectic manifolds of Kodaira dimension 0. I will describe work
adressing these questions in the genus 0 case.

**
Chart description for hyperelliptic Lefschetz fibrations and their stabilization
(by Hisaaki Endo) **

**Abstract****:**

Chart descriptions
are a graphic method to describe monodromy representations of various
topological objects. Here we introduce a chart description for hyperelliptic
Lefschetz fibrations, and show that any hyperelliptic Lefschetz fibration can be
stabilized by fiber-sum with certain basic Lefschetz fibrations. This is a joint
work with Seiichi Kamada.

**
Two variants of the 10/8 inequality (by Mikio Furuta) **

**Abstract****:**

(1) A
generalization of spin(^c) structure: Using SO(3)-instantons Froyshov showed a
local coeffiecient version of Donaldson's theorem about definite intersection
form. Using a local coefficient version of Seiberg-Witten monopoles Nakamura
showed a similar result as well as a 10/8-type inequiality. I will explain a
slight improvement of Nakamura's inequality. Joint work with Yukio Kametani and
Nobuhiro Nakamura. (2) Spin manifolds with boundary: Two invariants
$\omega_+,\omega_-$ for spin homology 3-spheres are introduced in terms of
Pin(2)-equivariant Floer K group to formulate 10/8 type inequality for spin
4-manfolds with boundary. A similar result is obtained by Manolescu
independently. I will explain an estimate of $\omega_+,\omega_-$ for Seifert
fibered cases. Joint work with Tian-Jun Li.

**
Exotic smoothings of open 4-manifolds (by Robert Gompf) **

**Abstract****:**

Smoothing theory
for open 4-manifolds seems to have stagnated in the past decade or two, perhaps
due to the misperception that since everything probably has uncountably many
smoothings, that must be the end of the story. However, most traditional
approaches involve tinkering with the end of the manifold without probing the
deeper structure such as minimal genera of homology classes. We show that this
genus function, together with its counterpart at infinity, can be controlled
surprisingly well compared to the case of closed 4-manifolds, and these tools
are often complementary to traditional techniques.

**
Homology classes of negative square and embedded surfaces in 4-manifolds (by
Mark Hamilton) **

**Abstract****:**

Problem 4.105 from
the Kirby list asks if the self-intersection number of embedded spheres in any
given simply-connected closed oriented 4-manifold X is always greater than some
negative number depending only on X. We can consider the same question for
embedded surfaces of arbitrary fixed genus. We will answer a part of this
question and show that there is such a lower bound in the case that the homology
class represented by the surface is divisible or characteristic.

**
Heegaard Floer homology and numerical semigroups (by Cagri Karakurt)
**

**Abstract****:**

Recently, Nemethi
gave a combinatorial description of Heegaard Floer homology for a class of
3-manifolds containing all Seifert fibered spaces. I will talk about a
reformulation of this description in terms of some numerical semigroups
generated by Seifert invariants. This is a joint work with Mahir Bilen Can.

**
Slice versus ribbon for some fibered knots (by Hee-Jung Kim) **

**Abstract****:**

In 1983, Casson and
Gordon showed that a fibered ribbon knot has monodromy that (when capped off)
extends over a handlebody. Shortly afterwards, Bonahon gave an infinite
collection of genus 2 fibered knots K_n, and analyzed the cobordism
classification of their monodromies. As a consequence, he showed (via the
Casson-Gordon result) that K_m # -K_n is ribbon if and only if m=n. We
investigate whether these knots can be slice, as a test of the `slice implies
ribbon' conjecture, and show that K_m # -K_0 is slice if and only if m =0. This
is a joint work with Daniel Ruberman.

**
Invariants from Seiberg-Witten and Heegaard Floer theory (by Yi-Jen Lee)
**

**Abstract****:**

**
Heegaard Floer homology of Seifert fibered homology spheres and non-zero degree
maps (by Tye Lidman) **

**Abstract****:**

Using a recent
combinatorial description of the Heegaard Floer homology of Seifert fibered
homology spheres due to Can and Karakurt, we study the behavior of these objects
under non-zero degree maps. This is joint work with Cagri Karakurt.

**
The triangulation conjecture (by Ciprian Manolescu) **

**Abstract****:**

We define
Pin(2)-equivariant Seiberg-Witten Floer homology for rational homology 3-spheres
equipped with a spin structure. The analogue of Froyshov'’s correction term in
this setting is an integer-valued invariant of homology cobordism whose mod 2
reduction is the Rokhlin invariant. As an application, we show that the
3-dimensional homology cobordism group has no elements of order 2 that have
Rokhlin invariant one. By previous work of Galewski-Stern and Matumoto, this
implies the existence of non-triangulable high-dimensional manifolds.

**
Applications of 4-dimensional techniques to Dehn surgery (by Yi Ni)
**

**Abstract****:**

In recent years,
techniques from 4-dimensional topology have been used to study many classical
problems in Dehn surgery. I will talk about one of such applications.

**
Symplectic fillings of lens spaces as Lefschetz fibrations (by Burak Ozbagci)
**

**Abstract****:**

We construct a
positive allowable Lefschetz fibration over the disk on any minimal weak
symplectic filling of the canonical contact structure on a lens space. Using
this construction we prove that any minimal symplectic filling of the canonical
contact structure on a lens space is obtained by a sequence of rational
blowdowns from the minimal resolution of the corresponding complex
two-dimensional cyclic quotient singularity. (This is a joint work with Mohan
Bhupal)

**
Hamiltonian Groups as Lie Groups (by Martin Pinnsonault) **

**Abstract****:**

Let M be a compact,
connected, symplectic manifold. Because the group Ham(M) of Hamiltonian
diffeomorphisms of M admits a bi-invariant metric, it is tempting to look for
analogies between properties of Ham(M) and properties of finite dimensional Lie
groups. In this talk, I will present 3 different analogies that lead to
interesting results if we assume M is toric.

**
Symplectic Fillings of Seifert Fibered Spaces over the 2-sphere (Laura
Starkston) **

**Abstract****:**

The goal of this
talk is to explain how to obtain a finite list of possible diffeomorphism types
of symplectic fillings of a large class of Seifert fibered spaces over S^2 with
their canonical contact structures. In many cases all of these diffeomorphism
types can be realized as strong symplectic fillings, thus providing some
complete classifications. The main arguments in the proof generalize those used
by Lisca to classify symplectic fillings of Lens spaces with their standard
contact structure. The technique is constructive and can suggest new
diffeomorphism types that support a convex symplectic structures. Combinatorial
analysis of the Seifert invariants, produces handlebody diagrams for the
possible diffeomorphism types of symplectic fillings. These alternate fillings
seem to all have smaller Euler characteristic than the standard filling given by
a plumbing of spheres. Such fillings can provide operations on closed symplectic
manifolds that generalize rational blow-downs

**
Higher dimensional contact manifolds (by Andras Stipsicz) **

**Abstract****:**

We discuss the
existence problem of contact structures on closed manifolds with odd dimension.
In particular, we show that for a 4-manifold X the product XxS^1 is contact
(joint with HJ Geiges) and using surgery theoretic methods we show that if M is
contact, then so is MxS^2. This is joint work with Jonathan Bowden and Diarmuid
Crowley.

**
The mu-bar invariants and the eta invariants for Seifert rational homology
3-spheres (by Masaaki Ue) **

**Abstract****:**

We discuss the
relation between the mu-bar invariants defined by Neumann and Siebenmann and the
eta invariants for the Dirac and the signature operators for Seifert rational
homology 3-spheres. Our arguments are based on the finite dimensional
approximation of the Seiberg-Witten invariants by Furuta.

**
Lagrangian submanifolds of CP^n (by Michael Usher) **

**Abstract****:**

**
Quasi-homomorphisms on mapping class groups (by Jiajun Wang) **

**Abstract****:**

A
quasi-homomorphism on a group is a real-valued function which is a homomorphism
up to a constant. Quasi-homomorphisms on the mapping class groups of surfaces
include signature, linking number, Rasmussen invariant, Ozsvath-Szabo
invariants, etc. We show that the quasi-homorphisms on a surface vanishing on
the handlebody group is an infinite-dimensional vector space. As an application,
we disprove a conjecture of Reznikov, which says that the set of Heegaard
splittings with a given genus has a bounded generation. This is a joint work
with Jiming Ma.

**Abstract****:**

The problem of
symplectic ball-packing has been one of the most important problems in
symplectic geometry, especially in dimension 4. In this talk we summarize some
recent developments on some aspects other than studying the packing capacity.
This will include some new results on symplectic mapping class groups and
Lagrangian uniqueness on symplectic 4-manifolds.

**Abstract****:**

In this talk, we
will discuss recent progress on the 3-dimensional analogue of
Thom-conjecture-type questions. In particular, we show that a simple knot in a
lens space is genus minimizing within its homology class. This is a joint work
with Yi Ni.

**Abstract****:**

After explaining
complexity of arbitrary reducible subvariety when the ambient manifold is of
dimension 4, we offer an upper bound of the total genus of a J-holomorphic
subvariety when the class of the subvariety is J-nef. It seems new even when J
is integrable. For a spherical class, it has particularly strong consequences.
It is shown that, for any tamed J, each irreducible component is a smooth
rational curve. We completely classify configurations of maximal dimension. To
prove these results, we treat subvarieties as weighted graphs and introduce
several combinatorial moves. This is a joint work with Tian-Jun Li.

- Bahar Acu (University of Southern California)
- Selman Akbulut (Michigan State)
- Anar Akhmedov (University of Minnesota)
- Yahya Almalki (Florida State University)
- Mehmet Firat Arikan (Middle East Technical University)
- Aykut Arslan (Michigan State)
- Dave Auckly (Kansas State University)
- Inanc Baykur (Max Planck Institute)
- Julia Bennett (University of Texas, Austin)
- Karatug Ozan Bircan (Koc University)
- Edward Burkard (University of Notre Dame)
- Robert Castellano (Columbia University)
- Daniele Celoria (University of Florence)
- Weimin Chen (University of Massachusetts, Amherst)
- Tim Cochran (Rice University)
- Josef Dorfmeister (North Dakota State University)
- Daniel Selahi Durusoy (Michigan State University)
- Ilknur Egilmez (University of Southern California)
- Hisaaki Endo (Tokyo Institute of Technology)
- Wei Fan (Michigan State)
- Yoshihiro Fukumoto (Ritsumeikan University)
- Mikio Furuta (University of Tokyo)
- Robert Gompf (University of Texas, Austin)
- Mark Hamilton (University of Stuttgart)
- Daniel Herr (University of Massachusetts)
- Chung-I Ho (NCTS)
- Jennifer Hom (Columbia University)
- Gao Hongzhu (Beijing Normal University)
- Henry Horton (Indiana University)
- Mustafa Kalafat (Tunceli University)
- Cagri Karakurt (University of Texas, Austin)
- Kaveh Kasebian (Michigan State University)
- Tirasan Khandhawit (MIT)
- John Kilgore (University of Minnesota)
- Hee Jung Kim (Max Planck Institute)
- Adam Knapp (Columbia University)
- Kyle Larson (University of Texas, Austin)
- Oleg Lazarev (Stanford University)
- Yi-Jen Lee (The Chinese University of Hong Kong)
- Hongxia Li (University of Minnesota)
- Tian-Jun Li (University of Minnesota)
- Youlin Li (Georgia Tech)
- Tye Lidman (University of Texas, Austin)
- Jianfeng Lin (University of California, Los Angeles)
- Francesco Lin (MIT)
- Yajing Liu (University of California, Los Angeles)
- Surya Thapa Magar (Kansas State University)
- Mak Cheuk Yu (University of Minnesota)
- Ciprian Manolescu (University of California, Los Angeles)
- Jeffrey Meier (University of Texas, Austin)
- Sergey Melikhov (Steklov Math. Institute and IAS)
- Nobuhiro Nakamura (Gakushuin University)
- Yi Ni (Caltech)
- Burak Ozbagci (Koc University)
- Heesang Park (KIAS)
- JungHwan Park (Rice University)
- Martin Pinsonnault (University of Western Ontario)
- Juanita Pinzon (Indiana University)
- Nasrin Sadegh Zadeh (University of Qom)
- Kadriye Nur Saglam (University of Minnesota)
- Sumeyra Sakalli (University of Minnesota)
- Christopher Scaduto (University of California, Los Angeles)
- Cotton Seed (Princeton University)
- Hirofumi Sasahira (Nagoya University)
- Dongsoo Shin (Chungnam National University)
- Igor Shnurnikov (Yaroslav State University)
- Kyler Siegel (Stanford University)
- Laura Starkson (University of Texas, Austin)
- Andras Stipsicz (Renyi Institute)
- Matthew Stoffregen (University of California, Los Angeles)
- Moto Tange (University of Tsukuba)
- Oliver Thistlethwaite (University of California, Riverside)
- Eamonn Tweedy (Rice University)
- Masaaki Ue (Kyoto University)
- Michael Usher (University of Georgia)
- Faramarz Vafaee (Michigan State)
- Diego Vela (Rice University)
- Jiajun Wang (Peking University)
- Chris Wendl (University College London)
- Luke Williams (Michigan State)
- Biji Wong (Brandeis University)
- Weiwei Wu (Michigan State)
- Zhongtao Wu (Caltech)
- Pengcheng Xu (Oklahoma State University)
- Kouichi Yasui (Hiroshima University)
- Eylem Zeliha Yildiz (Michigan State)
- Weiyi Zhang (University of Michigan)
- Yongsheng Zhang (Stony Brook University)
- Jingyu Zhao (Columbia University)
- Changwei Zhou (Binghamton University)
- Ke Zhu (Harvard University)
- Alex Zupan (University of Texas, Austin)