Topology in Australia and South Korea

The University of Melbourne, May 1 – 5, 2017

A conference to foster connections among topologists in the Asia-Pacific region.

Lecture Series

There will be a pair of three-hour lecture series on topics of current interest. The first will be given by Mike Hopkins, and the second will be given by Yong-Geun Oh.

Speakers

In addition to the lecture series, there will be a number of one-hour research talks. Currently confirmed speakers include Cheol-Hyun Cho, Zsuzsanna Dancso, Byeongho Lee, Daniel Murfet, Seonjeong Park, and Craig Westerland.

Location

The conference will be held at the Parkville campus of The University of Melbourne, in the Peter Hall building.

Abstracts

Title TBA.

Mike Hopkins (Harvard)

Abstract TBA.

Lagrangian Floer theory and mirror symmetry on toric manifolds

Yong-Geun Oh (IBS-CGP)

In this lecture series, I will explain how Lagrangian Floer theory works on compact toric manifolds from the point of view of homological mirror symmetry. I will explain a description of Fukaya category of toric manifolds in terms of special collection of Lagrangian fibers and explain the isomorphism between the Frobenius structures of quantum cohomology of toric manifolds and Saito's theory of singularities of the (Landau-Ginzburg) potential function. This lecture is based on the joint works with Fukaya, Ohta and Ono.

Globalizing local mirror functors

Cheol-Hyun Cho (Seoul National University)

We explain a (local) homological mirror functor formalism using a single Lagrangian L in a symplectic manifold, which we call local mirror functors. This gives an A-infinity functor from Fukaya category to the matrix factorization category of the potential function of L. In the case of punctured Riemann surfaces, these local functors can be glued to obtain a global mirror, which is a Landau-Ginzburg model on toric Calabi-Yau manifold. This is a joint work in progress with Hansol Hong and Siu-Cheong Lau.

Categorified and quantized lattices of integer cuts and flows

Zsuzsanna Dancso (University of Sydney)

Given a finite graph G, I will present a homological algebraic construction which realizes the lattices of integer cuts and flows of G, as parts of the Groethendieck group of a certain module category. Relevant graph theoretic objects will be defined. We'll then discuss dreams and open questions: a theory of quantized lattices, categorical lattice gluing, possible applications to topology. Joint work in progress with Anthony Licata.

Cohomological rigidity of manifolds arisen from right-angled 3-dimensional polytopes

Seonjeong Park (OCAMI)

A family of closed manifolds is called cohomologically rigid if a cohomology ring isomorphism implies a diffeomorphism for any two manifolds in the family. In this talk, we present a recent result on cohomological rigidity for large families of 3-dimensional and 6-dimensional manifolds defined by right-angled 3-dimensional polytopes. We consider the class 𝒫 of 3-dimensional combinatorial simple polytopes P, different from a tetrahedron, whose facets do not form 3-belts or 4-belts. By a theorem of Pogorelov, each polytope from 𝒫 admits a right-angled realization in Lobachevsky 3-space, which is unique up to isometry. Our families of smooth manifolds are associated with polytopes from the class 𝒫. The first family consists of 3-dimensional small covers of polytopes from 𝒫, or hyperbolic 3-manifolds of Löbell type. The second family consists of 6-dimensional quasitoric manifolds over polytopes from 𝒫. This talk is based on the joint work with Buchstaber, Erokhovets, Masuda, and Panov.

Structure theorems for braided Hopf algebras

Craig Westerland (Minnesota)

The Poincaré-Birkhoff-Witt and Milnor-Moore theorems are fundamental tools for understanding the structure of Hopf algebras. Part of the classification of pointed Hopf algebras involves a notion of “braided Hopf algebras.” I will present recent work which establishes analogues of the Poincaré-Birkhoff-Witt and Milnor-Moore theorems in this setting. The main new tool is a braided analogue of a Lie algebra defined in terms of braided operads. This can be used to establish these results, as well as a proof of the Andruskiewitsch-Schneider conjecture on generation of pointed Hopf algebras. Additionally, there appears to be an unexpected connection to profinite braid groups and related operads.

Participants

Name Affiliation
Vigleik Angeltveit Australian National University
Mirela Babalic IBS Center for Geometry and Physics
Bea Bleile University of New England
Imre Bokor
Clarisson Rizzie Canlubo University of the Philippines-Diliman
Cheol-Hyun Cho Seoul National University
Diarmuid Crowley University of Melbourne
Zsuzsanna Dancso University of Sydney
Dmitry Doryn IBS Center for Geometry and Physics
Gabriel C. Drummond-Cole IBS Center for Geometry and Physics
Nora Ganter University of Melbourne
Philip Hackney Macquarie University
Mike Hopkins Harvard University
Calin Lazaroiu IBS Center for Geometry and Physics
Byeongho Lee National Institute for Mathematical Sciences
Eon-Kyung Lee Sejong University
Sang-Jin Lee Konkuk University
Daniel Lin Macquarie University
Daniel Murfet University of Melbourne
Csaba Nagy University of Melbourne
Yong-Geun Oh IBS Center for Geometry and Physics
Seonjeong Park Osaka City University Advanced Mathematical Institute
Marcy Robertson University of Melbourne
TriThang Tran Monash University
Craig Westerland University of Minnesota
Albert Zhang University of Melbourne

Registration information

Registration should be done by filling out this form. In case a formal letter of invitation is required, please also email the organizers at asiapacifictopology@gmail.com and provide date of birth, nationality, contact phone number and a brief CV.

Registration Fee

As a condition on our funding, we are required to collect a fee for attendance at the conference. The registration fee of 25 AUD will be collected at the conference itself.

Visas

Most international participants will need a visa to enter Australia, and should consult the website of the department of immigration and border protection for more information.

AMSI Travel Fund

This event is sponsored by the Australian Mathematical Sciences Institute (AMSI). AMSI allocates a travel allowance annually to each of its member universities (for list of members, see http://amsi.org.au/membership/members)

Students or early career researchers from AMSI member universities without access to a suitable research grant or other source of funding may apply to the Head of Mathematical Sciences for subsidy of travel and accommodation out of the departmental travel allowance.


Organized by Vigleik Angeltveit, Gabriel C. Drummond-Cole, Philip Hackney, and Marcy Robertson.
We are grateful for support from:

Australian Mathematical Sciences Institute
Institue for Basic Science