| July 20 (Thu) | July 21 (Fri) | July 22 (Sat) | |
|---|---|---|---|
| 07:30 ~09:00 | Breakfast | Breakfast | |
| 09:30 ~10:30 | Talk P2 Junyong Park |
Talk Dr. JuA Lee |
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| 10:30 ~10:50 | Coffee break | Coffee break | |
| 10:50 ~11:50 | Talk Dr. Kyungbae Park |
Talk Prof. Ki-Heon Yun |
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| 12:00 ~14:00 | Lunch | Lunch | Lunch |
| 14:30 ~15:30 | Talk Prof. Jongil Park |
Talk Dongheon Choe |
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| 15:30 ~15:50 | Coffee Break | Coffee Break | |
| 15:50 ~16:50 | Talk P1 Junyong Park |
Talk Hakho Choi |
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| 16:50 ~17:00 | Coffee break | Coffee break | |
| 17:00 ~18:00 | Talk Dr. Youngho Yoon |
Discussion | |
| 18:00 ~19:30 | Dinner | Dinner |
Title: Smoothly embedded rational homology 4-balls
Abstract: In this talk I’d like to explain the existence of rational homology 4-balls smoothly embedded in regular neighborhoods of certain linear chains of smooth 2-spheres by using techniques from minimal model program for 3-dimensional complex algebraic variety.
Title: Lefschetz fibrations on smooth 4-manifolds and Rational blow up & down by lantern relations
Abstract: Morse theory is amazingly useful for understanding the smooth manifolds. The complex analogue of the Morse theory on smooth 4-manifolds is the notion of Lefschetz fibrations. We will take a tour through symplectic 4-manifolds by focusing on the Lefschetz fibrations of genus 1 and genus 2 which formed the templates for many of the beautiful constructions. We will be accompanied by the mapping class groups of surfaces which allows us to not only see the singular fibers and their arrangements but also allows us to move between different smooth structures via rational blowdown topological surgery that can be performed algebraically by lantern relation substitutions.
Title: Hodge spectrum of hypersurface singularity
Abstract: Milnor fiber gives invariants of complex hypersurface singularities. Monodromy and Hodge structure on the cohomology of Milnor fiber are important analytic invariants of hypersurface singularities. Hodge spectrum encodes partial but important data of these. We will see how we can recover classical invariants and how we can calculate the spectrum for special cases.
Title: Topology & Arithmetic of moduli for fibered surfaces and heuristics for counting elliptic & hyperelliptic curves over global fields
Abstract: The notions of fibrations lie at the heart of the Enriques-Kodaira classification of complex surfaces as well as the Mumford-Bombieri classification of algebraic surfaces in positive characteristics. We will take a tour through algebraic surfaces by formulating the moduli of Lefschetz fibrations and finding the arithmetic invariant of the moduli over the finite fields. Along the way, I would like to discuss the language of moduli stacks in terms of the moduli of curves and surfaces. Our tour of moduli of fibered surfaces will end with acquiring the heuristics for counting elliptic and hyperelliptic curves over the global function &number fields.
Title: On quasi-alternating links and definite 4-manifolds
Abstract: In the context of Heegaard Floer theory, quasi-alternating (QA) links are a generalization of the class of alternating links. They share many properties with alternating links. For example, knot Floer and Khovanov homologies of a QA link are known to be thin (in other words, the homological invariants are simply determined by the signature, and Alexander and Jones polynomial of the link.) In this talk, we review how definite 4-manifolds have been used to the study of QA links, such as the existence of homologically thin, non-QA link, the classification QA Montesinos links, and so on.
Title: Spherical 3-manifolds which bound rational homology balls
Abstract: We consider the question of which 3-manifolds bound rational homology 4-ball. In this talk, I’ll review the results on lens spaces, some family of Seifert fibered 3-manifolds and manifolds given by Dehn surgery on a knot in . Finally, I’ll focus on 3-manifolds with finite fundamental group by using correction term invariants by Ozsvath and Szabo.
Title: Symplectic fiilings of links of non cyclic quotient surface singularities as lefschetz fibration
Abstract: The link of quotient surface singularities admit natural contact structure, so called Milnor fillable contact structure . Minimal symplectic fillings are classified by Lisca for cyclic quotient singularities and Bhupal-Ono for non-cyclic quotient singularities. On the otherhand, Heesang Park, Jongil Park, Dongsoo Shin, and Giancarlo Urzua showed that, for the quotient surface singularities, every (minimal) symplectic filling is diffeomorphic to a Milnor fiber. Since Milnor fibers has a natural Stein structure, there is a corresponding PALF structure on each symplectic filling of . For the cyclic quotient surface singularities, Burak Ozbacgi and Mohan Bhupal found an algorithm for PALF structure on symplectic filling of and showed that they are related by a sequence of Rational blow downs. In this talk we give generalization of Ozbacgi-Bhupal’s work to the Dihedral case.
Title: Studies on geography of Lefschetz fibrations over a two sphere
Abstract: I will talk about the known results about the Geography problem of relatively minimal Lefschetz fibrations over a two sphere.
Title: Minimal number of singular fibers in Lefschetz fibration and related topics
Abstract: In the talk I will briefly review some well known results about the minimal number of singular fibers in Lefschetz fibrations over a surface. After that I will explain some related (open) problems in the geography of symplectic Lefschetz fibration.