July 30 to August 11, 2012

Stanford University

**Organizers:** S. Akbulut (MSU) , A. Akhmedov (UMN), D. Auroux (Berkeley), Y. Eliashberg (Stanford), K. Honda (USC), C. Karakurt (UT Austin), P. Ozsváth (Princeton).

- Selman Akbulut (Michigan State)
- Yasha Eliashberg (Stanford)
- Sergei Gukov (Caltech)
- Ko Honda (USC)
- Robert Lipshitz (Columbia)
- Katrin Wehrheim (MIT)

**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.

**Symplectic topology of Weinstein manifolds (by Yasha Eliashberg)**

**Abstract****:**

Weinstein manifolds are symplectic counterparts of affine complex manifolds. We discuss in the lectures techniques (due to Bourgeois, Ekholm and the lecturer) for computation of symplectic invariants of Weinstein manifolds via their handlebody decompositions.

** The geometry and physics of Knot Homologies (by Sergei Gukov)**

**Abstract****:**

**HF=ECH via open book decompositions (by Ko Honda)**

**Abstract****:**

The goal of this minicourse is to give a brief introduction to Heegaard Floer homology (due to Ozsvath-Szabo) and embedded contact homology (due to Hutchings), and to prove the equivalence between the two homology theories. The equivalence is joint work with Vincent Colin and Paolo Ghiggini.

**Computing with bordered Heegaard Floer homology (by Robert Lipshitz)**

**Abstract****:**

Heegaard Floer homology is an extension of the Seiberg-Witten invariants of closed 4-manifolds to invariants of closed 3-manifolds and 4-manifolds with boundary. Bordered Heegaard Floer homology is a further extension, to closed surfaces and 3-manifolds with boundary. We will start by discussing the formal structure of bordered Heegaard Floer homology and discuss how it is defined in a toy model. We will then sketch the definitions in general and spend the rest of the time discussing various ways it can be used for computations. (This is joint work with Peter Ozsvath and Dylan Thurston.)

**Pseudoholomorphic quilts and low dimensional topology (by Katrin Wehrheim)**

**Abstract****:**

I will give an introduction to Lagrangian correspondences and
holomorphic quilts, their analysis, and some sample applications in
both symplectic topology and the construction of 3- and 4-manifold
invariants.

**Short talks :**

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

For direction to the Stanford Mathematics Department, please click here

Monday 7/30 | Tuesday 7/31 | Wednesday 8/1 | Thursday 8/2 | Friday 8/3 |

9:00-9:30 Registration and Coffee |
9:00-9:30 Coffee |
9:00-9:30 Coffee |
9:00-9:15 Coffee |
9:00-9:30 Coffee |

9:30-10:30 Eliashberg I |
9:30-10:30 Honda II |
9:30-10:30 Gukov I |
9:15-10:15 Gukov II |
9:30-10:30 Lipshitz III |

11:00-12:00 Honda I |
11:00-12:00 Lipshitz I |
11:00-12:00 Honda III |
10:30-11:30 Wehrheim II |
11:00-12:00 Wehrheim III |

Lunch | Lunch | Lunch | 11:45-12:45 Akbulut III |
Lunch |

2:00-3:00 Akbulut I |
2:00-3:00 Akbulut II |
2:00-3:00 Lipshitz II |
2:45-5:45 Short talks |
2:00-3:00 Gukov III |

3:30-4:30 Eliashberg II |
3:30-4:30 Wehrheim I |
3:30-4:30 Eliashberg III |
||

5:00 Math Department courtyard |

Monday 8/6 | Tuesday 8/7 | Wednesday 8/8 | Thursday 8/9 | Friday 8/10 | Saturday 8/11 |

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 Taubes |
9:30-10:30 Stipsicz |
9:00-10:00 Ekholm |
9:30-10:30 Akbulut |
9:30-10:30 Bourgeois |
9:00-10:00 Akhmedov |

11:00-12:00 Gukov |
11:00-12:00 Hedden |
10:15-11:15 Ng |
11:00-12:00 Wendl |
11:00-12:00 Abreu |
10:15-11:15 Borman |

Lunch | Lunch | 11:30-12:30 Woodward |
Lunch | Lunch | 11:30-12:30 Cornea |

1:30-2:30 Perutz |
1:30-2:30 Manolescu |
free afternoon |
1:30-2:30 Hutchings |
1:30-2:30 McLean | |

2:45-3:45 Lekili |
2:45-3:45 Ghiggini |
2:45-3:45 Yasui |
2:45-3:45 Entov | ||

4:15-5:15 Thurston |
4:15-5:15 Hom |
4:15-5:15 Ozbagci |
4:15-5:15 Plamenevskaya |
||

6:30 at Ming's restaurant |

**Titles and abstracts of the talks :**

** Displacing Lagrangian toric fibers by extended probes (by Miguel Abreu)**

**Abstract****:**

I will address a natural Lagrangian intersection problem in the context
of toric symplectic manifolds (and orbifolds): displaceability of Lagrangian torus orbits. I will start with joint work with Leonardo Macarini on a
symplectic reduction interpretation of known non-displaceability results, and will then describe more recent joint work with Matthew Strom Borman
and Dusa McDuff, introducing extended probes as a generalization of McDuff's displaceability method of probes. I will finish with applications in
several examples, including some simple ones with continuous sets of Lagrangian torus orbits whose displaceability status is unknown.

**Corks, plugs, Glucks, and ropes (by Selman Akbulut)**

**Abstract****:**

Corks and plugs are small fundamental pieces in smooth 4-manifolds which determine their smooth structure (twisting along them changes smooth structure). Roughly cork-twisting is related altering Floer homology, while plug-twisting is related to altering Spin^c structures. Also plug-twisting generalizes the Gluck-twisting operation. I will review some of the recent joint work with K.Yasui about them. There are also big alterations of 4-manifolds, by taking big chunks out and re-glueing them back, which can result change the smooth structures. A. Akhmedov and B. D. Park used this kind of operation to construct small exotic manifolds without boundary. Breaking these chunks into small corks is an open problem (although theoretically it is possible). One way to perform such operation on a handlebody is by what we call the "roping'' technique (imagine hanging shirts on hangers in a dress closet and then keep rearranging them, one way to recall where they were before is to connect them by ropes to one central hook on the ceiling then do rearranging).

** Exotic 4-manifolds with small Euler characteristics (by Anar Akhmedov)**

**Abstract****:**

It is known that many simply connected, smooth topological 4-manifolds admit infinitely many exotic smooth structures. However, the smaller the Euler characteristic, the harder it is to construct exotic smooth structure. In this talk, we will construct exotic smooth structures on various small 4-manifolds. We will also discuss interesting applications to the geography of spin and non-spin symplectic 4-manifolds. This is mostly a joint work with B. Doug Park.

**The size of a Weinstein neighborhood of a Lagrangian (by Matthew Borman)**

**Abstract****:**

The width of a Lagrangian is the largest capacity of ball that can be symplecticly embedded into the ambient manifold such that the ball intersects the Lagrangian exactly along the real part of the ball. This notion provides a quantitative answer to the question "What is the maximal size of a Weinstein neighborhood for the Lagrangian?" In this talk I will present a wrapped Floer cohomology construction that can upper bound a Lagrangian's width in terms of its displacement energy. This is joint work in progress with Mark McLean.

** S^1-equivariant symplectic homology and linearized contact homology (by Frederic Bourgeois)**

**Abstract****:**

We define an S^1-equivariant version of symplectic homology via various equivalent approaches. We show that, over rational coefficients, S^1-equivariant symplectic homology is isomorphic to linearized contact homology. This is joint work with Alexandru Oancea.

** Lagrangian Cobordism and Categorification (by Octav Cornea)**

**Abstract****:**

I will discuss recent work joint with Paul Biran (ETH) on the existence and properties of a functor relating a certain Lagrangian cobordism category and the derived Fukaya category.

** Exact Lagrangian immersions with a single double point (by Tobias Ekholm)**

**Abstract****:**

We show that if a closed orientable 2k-manifold K, k > 2,
with Euler characteristic not equal to −2 admits an exact Lagrangian immersion
into complex 2k-space with one transverse double point and no
other self intersections, then K is diffeomorphic to the sphere. The proof
combines Floer homological arguments with a detailed study of moduli
spaces of holomorphic disks with Lagrangian boundary conditions determined
by K. We will also discuss related results in the odd dimensional
case. The talk reports on joint work with Ivan Smith.

** Symplectic rigidity and the Poisson bracket (by Michael Entov)**

**Abstract****:**

The Poisson bracket of two smooth functions on a symplectic
manifold depends on their first derivatives. Nevertheless, as it has been
discovered in "hard" symplectic topology in recent years, the Poisson
bracket is rather sensitive to the uniform (that is, C^0) norm of
functions. I will discuss a new manifestation of this phenomenon and its
application to Hamiltonian dynamics, based on a joint work with L.Buhovsky
and L.Polterovich.

** Knot filtrations in embedded contact homology (by Paolo Ghiggini)**

**Abstract****:**

Embedded contact homology is a Floer theoretic invariant of three-manifolds which is isomorphic to Heegaard Floer homology by the work of Kutluhan, Lee and Taubes and of Colin, Ghiggini and Honda. An important feature of Heegaard Floer homology is the existence of a knot filtration associated to any knot in a three-manifold. I will describe two equivalent ways to construct a similar filtration in embedded contact homology and discuss some conjectures and corollaries. This is a joint work with V. Colin, K. Honda and M. Hutchings.

** Super-A-polynomial (by Sergei Gukov)**

**Abstract****:**

The generalized volume conjecture states that "color dependence" of the
colored Jones polynomial is governed by an algebraic variety, the zero
locus of the A-polynomial (for knots) or, more generally, by character
variety (for links or higher-rank quantum group invariants). This relation,
based on SL(2,C) Chern-Simons theory, explains known facts and predicts
many new ones.
In particular, since the colored Jones polynomial can be categorified to a
doubly-graded homology theory, one may wonder whether the generalized (or
quantum) volume conjecture admits a natural categorification. In this talk,
I will argue that the answer to this question is "yes" and introduce a
two-parameter deformation of the A-polynomial that describes the "color
behavior" of the HOMFLY homology, much like the ordinary A-polynomial does
it for the colored Jones polynomial.This deformation, named the
super-A-polynomial, is strong enough to distinguish mutants, and its most
interesting properties include relation to knot contact homology and knot
Floer homology.

** Recent progress on smooth concordance (by Matthew Hedden)**

**Abstract****:**

Call two knots concordant if they arise as the boundary of a
smooth and properly embedded cylinder in the three-sphere times an
interval. Concordance is an equivalence relation and, modulo concordance,
knots form an abelian group. One can define an analogous group in a
purely topological category, and the kernel of a natural homomorphism
between the groups is generated by so-called topologically slice knots:
those knots which bound topologically flat disks in the four-ball. These
knots are particularly interesting, as they highlight the distinction
between the smooth and topological categories in dimension four. In this
talk I'll review what is known about topologically slice knots, and provide
the first examples of such knots which represent (two-) torsion elements in
the concordance group. This is joint work with Se-Goo Kim and Charles
Livingston.

** Applications of the knot Floer complex to concordance (by Jennifer Hom)**

**Abstract****:**

We will discuss a concordance invariant, epsilon, associated to
the knot Floer complex, and use this invariant to better understand knot
concordance. In particular, by considering the knot Floer complex up to the
weaker relation of epsilon-equivalence, rather than filtered chain homotopy
equivalence, we can obtain a wealth of concordance information. We will
discuss applications of this approach, such as a new filtration on the
smooth concordance group and bounds on concordance genus.

**Embedded contact homology as a (symplectic) field theory (by Michael Hutchings)**

**Abstract****:**

We use Seiberg-Witten theory to complete embedded contact
homology to a functor defined on the category of contact 3-manifolds and
strong symplectic cobordisms between them. We give applications to
functoriality of the ECH contact invariant, and to ECH capacities of
certain closed symplectic four-manifolds.

** Symplectic topology of rational blowdowns (by Yanki Lekili)**

**Abstract****:**

We study some finite quotients of the A_n Milnor fibre which coincide with the Stein surfaces that appear in Fintushel and Stern's rational blowdown construction. We show that these Stein surfaces have no exact Lagrangian submanifolds by using the already available and deep understanding of the Fukaya category of the A_n Milnor fibre coming from homological mirror symmetry. On the contrary, we find Floer theoretically essential monotone Lagrangian tori, finitely covered by the monotone tori that we studied in the A_n Milnor fibre. We conclude that these Stein surfaces have non-vanishing symplectic cohomology. This is joint work with M. Maydanskiy.

** Monopole Floer homology and covering spaces (by Ciprian Manolescu)**

**Abstract****:**

I will discuss a Smith-type inequality for regular covering spaces in monopole Floer homology. A corollary is that if an oriented 3-manifold Y admits a p^n-sheeted regular cover that is a Z/p-L-space (for p prime), then Y itself is a Z/p-L-space. This is joint work with Tye Lidman.

** On the symplectic invariance of log Kodaira dimension (by Mark Mclean)**

**Abstract****:**

Every smooth affine variety has a natural symplectic structure coming from some embedding in complex Euclidean space. This symplectic form is a biholomorphic invariant. An important algebraic invariant of smooth affine varieties is log Kodaira dimension. One can ask, to what extent is this a symplectic invariant? We show some partial symplectic invariance results for smooth affine varieties of dimension less than or equal to 3.

** Knot contact homology and the augmentation polynomial (by Lenhard Ng)**

**Abstract****:**

The augmentation polynomial is a three-variable knot invariant derived from knot contact homology. I will introduce this polynomial and some of its properties, including a proposed relation to the HOMFLY polynomial, and discuss its recent appearances in the physics literature.

** Singularity links with exotic Stein fillings (by Burak Ozbagci )**

**Abstract****:**

In a recent paper of Akhmedov-Etnyre-Smith-Mark, it was shown that certain contact
Seifert fibered 3-manifolds, each with a unique singular fiber, have infinitely many exotic simply-connected Stein fillings. Here we generalize this result to some contact Seifert fibered 3-manifolds with many singular fibers and observe that these 3-manifolds are links of some isolated complex surface singularities. In addition, we prove that the contact structures involved in the construction are the canonical contact structures on these singularity links. As a consequence we provide examples of isolated complex surface singularities whose links with their canonical contact structures have infinitely many exotic simply-connected Stein fillings---verifying a prediction of Andras Nemethi. For some of these singularity links, and for each positive integer n, we also construct an infinite family of exotic Stein fillings whose fundamental group is Z x Z_n. (This is a joint work with Anar Akhmedov).

** The arithmetic geometry of homological mirror symmetry (by Timothy Perutz)**

**Abstract****:**

Joint work with Yanki Lekili (Cambridge). Homological mirror symmetry (HMS) envisions an algebro-geometric interpretation of the Fukaya category of a polarized Calabi-Yau manifold X. The categories in question are defined over algebraically closed fields containing the complex numbers. The choice of an ample divisor in X makes available (in principle) a version of the Fukaya category defined over the much smaller ring of rational power series with integer leading term (in some cases Z[[q]] suffices). The mirror should then be a scheme defined over this same ring - an * arithmetic * variety. We discuss conjectural arithmetic refinements to HMS, which we expect to be present in all dimensions. In the case of the 2-torus, we prove that the Fukaya category relative to a point is derived-equivalent, over Z[[q]], to perfect complexes of coherent sheaves on the Tate curve, and that the * wrapped * Fukaya category of the complement of this point is derived-equivalent over Z to coherent sheaves on the Weierstrass curve * y^2 + xy = x^3 *.

** Flexibility properties of plastikstufes (by Olga Plamenevskaya)**

**Abstract****:**

In contact manifolds of dimension greater than 3, a plastikstufe (aka overtwisted family) is a possible generalization of an overtwisted disk. It is known that a contact manifold containing a plastikstufe cannot be fillable. We show that a plastikstufe also has some flexibility properties. In particular, under certain conditions, non-isotopic contact structures become isotopic after connect-summing with a sphere that contains a plastikstufe. (This is work in progress, joint with E. Murphy, K. Niederkruger, and A. Stipsicz.)

** Knots in Lattice homology (by Andras Stipsicz)**

**Abstract****:**

We introduce a filtration on the lattice homology of a negative definite plumbing tree associated to a further vertex and show how to determine
lattice homologies of surgeries on this last vertex. We discuss the relation with Heegaard Floer homology.

** SL(2;C) connections with L^2 bounds on curvature (by Clifford Taubes)**

**Abstract****:**

Non-Abelian gauge theories are used to study the structure of 3 and 4-dimensional spaces; and all such applications require a theorem of Karen Uhlenbeck about connections with integral bounds on their curvatures. Uhlenbeck's theorem only applies to a gauge theory with compact Lie group. I will describe an extension of Uhlenbeck's theorem that applies to gauge theories on 3-manifolds with the non-compact group SL(2,C). This extension will likely have analogs for the higher rank non-compact groups and it may have an analog for certain generalizations of the Seiberg-Witten equations. There is also a possibility that this extension will have an analog that can be used to define SL(2,C) Floer homology and SL(2,C) Donaldson invariants for 4-manifolds.

**
Tight but nonfillable contact manifolds in all dimensions (by Chris Wendl)**

**Abstract****:**

Contact topology in dimension three is shaped by the fundamental
dichotomy between "tight" and "overtwisted" contact structures, and
while it is not known whether any such dichotomy exists in higher
dimensions, there are certainly contact structures in all dimensions
that have all the trappings of overtwistedness (e.g. nonfillability,
vanishing contact homology), or tightness (e.g. no contractible
orbits, lack of flexibility). In dimension 3, the invariant known as
"Giroux torsion" has played a central role in classifying tight
contact structures, and in this talk I will explain how one can
generalize it to find the first examples in all dimensions of contact
structures that must be considered tight but do not admit any
symplectic fillings. A crucial ingredient for this is the existence
(also in all dimensions) of symplectic manifolds with disconnected
convex boundary, which requires a surprising digression into algebraic
number theory. This is joint work with Patrick Massot and Klaus
Niederkrueger.

** Non-displaceable Lagrangians and toric minimal model programs (by Christopher Woodward)**

**Abstract****:**

(w/ E. Gonzalez) We give a computation of the quantum cohomology of symplectic toric orbifolds which exhibits, for a toric minimal model program (tmmp), a splitting of the quantum cohomology so that each transition in the tmmp corresponds to a collection of Hamiltonian non-displaceable Lagrangian tori.

** Corks and exotic 4-manifolds (by Kouichi Yasui)**

**Abstract****:**

We discuss how to construct exotic 4-manifolds using corks. In particular, from any 4-dimensional compact oriented handlebody X without 3- and 4-handles and with b_2>0, we construct arbitrary many compact Stein 4-manifolds which are all
homeomorphic but mutually non-diffeomorphic, so that their topological invariants coincide with those of X. Time permitting we also construct exotic Stein fillings using log transform. This talk is based on joint work with Selman Akbulut.

- Tetsuye Abe (Kyoto University)
- Miguel Abreu (Instituto Superior Tecnico, Lisbon)
- Selman Akbulut (Michigan State)
- Anar Akhmedov (University of Minnesota)
- Firat Arikan (University of Rochester)
- Atanas Atansov (Harvard University)
- Denis Auroux (UC Berkeley)
- Russel Avdek (University of Southern California)
- Kerstin Baer (Stanford University)
- Ian Banfield (Boston College)
- Erkao Bao (University of Wisconsin)
- Stefan Bauer (University of Bielefled)
- Marzieh Bayeh (University of Regina)
- Inanc Baykur (Max Planck Institute)
- Ahmet Beyaz (Middle East Technical University)
- Mohan Bhupal (Middle East Technical University)
- Matthew Strom Borman (University of Chicago)
- Nate Bottman (MIT)
- Fredric Bourgeois (Universite Libre de Bruxelles)
- Mark Branson (Technion, Israel Institute of Technology)
- Olguta Buse (IUPUI)
- Haojie Chen (University of Minnesota)
- Weimin Chen (University of Massachusetts, Amherst)
- Dong Heon Choe (Seoul National University)
- Octav Cornea (University of Montreal)
- Christopher Cornwell (Duke University)
- Aliakbar Daemi (Harvard University)
- Alan Diaz (Georgia Tech)
- Josef Dorfmeister (North Dakota State University)
- David Duncan (Rutgers University)
- Daniel Selahi Durusoy (Grand Valley State University)
- Ilknur Egilmez (Koc University)
- Tobias Ekholm (Uppsala University)
- Yakov Eliashberg (Stanford University)
- Michael Entov (Technion-Israel Institute of Technology)
- Jacqueline Espina (University Lyon 1)
- Tolga Etgu (Koc University)
- Wei Fan (Michigan State University)
- David Farris (Indian Institute of Science, Bangalore)
- Ronald Fintushel (Michigan State)
- Urs Fuchs (Purdue University)
- Adina Gamse (Notheastern University)
- Saman Gharib (University of British Columbia)
- Paolo Ghiggini (University of Nantes)
- Sayonita Ghosh (University of Georgia)
- Allison Gilmore (Princeton University)
- Sergei Gukov (Caltech)
- Chen He (Northeastern University)
- Peng He (University of Pittsburg)
- Matthew Hedden (Michigan State)
- Daniel Herr (University of Massachussetts)
- Chung-I Ho (NCTS, Taiwan)
- Helmut Hofer (IAS, Princeton)
- Sonja Hohloch (Ecole Polytechnique Federale de Lausanne)
- Jennifer Hom (Columbia University)
- Ko Honda (USC)
- Ramon Horvarth (Uppsala University)
- Yang Huang (USC)
- Mark Hughes (Stony Brook)
- Michael Hutchings (UC Berkeley)
- Daniela Ijacu (University of Bucharest)
- Buban James (University of Califonia, Davis)
- Hwang Ji-Young (Sungshin Women's University)
- Amey Kaloti (Georgia Institute of Technology)
- Cagri Karakurt (University of Texas, Austin)
- Naohiko Kasuya (University of Tokyo)
- Keiko Kawamuro (University of Iowa)
- Do-Young Kim (Sungshin Women's University)
- Hee Jung Kim (POSTECH)
- Robion Kirby (UC Berkeley) (not confirmed)
- Mahdi Kouretchian (Sharif University of Technology)
- Thomas Kragh (MIT)
- David Krcatovich (Michigan State University)
- Cagatay Kutluhan (Harvard University)
- Sergii Kutsak (University of Florida)
- François Lalonde (University of Montreal)
- Kyle Larson (University of Texas at Austin)
- Juhyun Lee (Seoul National University)
- Ju A Lee (Seoul National University
- Jaepil Lee (Stony Brook)
- Heather Lee (UC Berkeley)
- Yanki Lekili (Cambridge University)
- Caitlin Leverson (Duke University)
- Adam Levine (Brandeis University)
- Sam Lewallen (Princeton University)
- Jiayong Li (MIT)
- Jun Li (University of Minnesota)
- Tian-Jun Li (University of Minnesota)
- Yi-Jen Li (Purdue University)
- Tye Lidman (UCLA)
- Vo Liem (University of Alabama)
- Ash Lightfoot (Indiana University)
- Robert Lipshitz (Columbia University)
- Yajing Liu (UCLA)
- Ligang Long (University of Texas at Austin)
- Adam Lowrance (University of Iowa)
- Ciprian Manolescu (UCLA)
- Gordana Matic (University of Georgia)
- Jason McGibbon (MIT)
- Mark McLean (MIT)
- Jeffrey Meier (University of Texas at Austin)
- Allison Moore (University of Texas at Austin)
- Chibili Nafaa (UAEU)
- Lenny Ng (Duke University)
- Khoa Lu Nguyen (Stanford University)
- Yi Ni (Caltech)
- Zhaohu Nie (Utah State University)
- Alexandru Oancea (University of Strasbourg)
- Christian Okonek (University of Zurich)
- Kaoru Ono (Hokkaido University)
- Burak Ozbagci (Koc University)
- Metin Özsarfati (Michigan State University)
- Peter Ozsvath (Princeton University)
- Heesang Park (Korea Institute for Advanced Study)
- B. Doug Park (University of Waterloo)
- Kyungbae Park (Michigan State University)
- James Pascaleff (University of Texas at Austin)
- Andrés Pedroza (Universidad de Colima)
- Alexander Perry (Harvard University)
- Timothy Perutz (University of Texas, Austin)
- Martin Pinsonnault (University of Western Ontario)
- Olga Plamenevskaya (Stony Brook)
- Lizhen Qin (Purdue University)
- Bela Racz (Princeton University)
- Ayesha Riasat (University Lahore)
- Yo'av Rieck (University of Arkansas)
- David Rose (Duke University)
- Daniel Ruberman (Brandeis University)
- Kadriye Nur Saglam (University of Minnesota)
- Dietmar Salamon (ETH Zurich)
- Sema Salur (University of Rochester)
- Masaya Sato (Kyushu University)
- Nikolai Saveliev (University of Miami)
- Yakov Savelyev (CRM-Montreal)
- Justin Scarfy University of British Columbia
- Felix Schmaschke (Max-Planck-Institute)
- Cotton Seed (Princeton University)
- Dongsoo Shin (Chungnam National University)
- Kyler Siegel (Stanford University)
- Peter Smillie (Harvard University)
- Laura Starkson (University of Texas at Austin)
- Andras Stipsicz (Renyi Institute)
- C-J Sung (National Tsing Hua University)
- Zack Sylvan (UC Berkeley)
- Clifford Taubes (Harvard University)
- Dylan Thurston (Columbia University)
- Surya Thapa Magar (Kansas State University)
- Yin Tian (University of Southern California)
- Bulent Tosun (Georgia Tech)
- Linh Truong (Princeton University)
- Siraj Uddin (University of Malaya)
- Selman Uguz (Harran University)
- Michael Usher (University of Georgia)
- Faramarz Vafaee (Michigan State University)
- Sushmita VenugoPalan (Rutgers University)
- Ramon Vera (Durham University)
- Renato Vianna (UC Berkeley)
- Katrin Wehrheim (MIT)
- Chris Wendl (University College London)
- Luke Williams (Michigan State University)
- Andrew Williams (University of Southern California)
- Biji Wong, (Brandeis University)
- Chris Woodward (Rutgers University, New Brunswick)
- Weiwei Wu (University of Minnesota)
- Zhongtao Wu (Caltech)
- Guangbo Xu (Princeton University)
- Andrew Yarmola (Boston College)
- Kouichi Yasui (Hiroshima University)
- Mei-Lin Yau (National Central University, Taiwan)
- Ustun Yildirim (Middle East Technical University)
- Alex Zamorzaev (Stanford University)
- Rumen Zarev (UC Berkeley)
- Bohua Zhan (Princeton)
- Weiyi Zhang (University of Michigan)
- Jie Zhao (University of Wisconsin at Madison)
- Qiao Zhou (Northwestern University)
- Ke Zhu (University of Minnesota)
- Seyed Zoalroshd (University of South Florida)

Thanks to the generous support of the National Science Foundation and the Stanford University Mathematics Research Center, funds are available for partial support of participant expenses. Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Applicants are requested to register, send a CV, including a brief description of research interests, and have one reference letter sent to akhmedov@math.umn.edu. The reference letter is optional for people more than two years after receiving a Ph.D. ***Please note that we are no longer accepting application*** .

Reservations for both single and shared housing, together with the travel dates . The website also includes information on housing check in, maps, and directions to your housing.

Please let us know if you wish to stay at the hotel. We have a special conference rate with the following hotel: The Cardinal Hotel (650)-323-5101.

The rates are as follows:

Standard rooms with private bath $125.00 + tax

Shared bath style rooms $75.00 + tax

Booking is subject to availability

Please follow this link for more information.

Here are some other useful links on housing:

Stanford Resources

The Munger Front Desk

Housing information if you are staying in a studio

Housing information if you are staying in a shared room

Please call the after-hours number to the location to be housed. The number is provided in each link provided. A staff member will meet the attendee to assist those arriving after 8pm. After 10pm, still call the after-hours number and a team member from HART (Housing After-Hours Response Team) will assist with check-in.

Maps & Directions to Stanford University