Title: Detection results in link Floer homology  Abstract: In this talk I will briefly describe link Floer homology toolbox and its usefulness. Then I will show how link Floer homology can detect links with small ranks, using a rank bound for fibered links by generalizing an existing result for knots. I will also show that stronger

Title: Symplectic fillings of lens spaces Abstract: Many contact 3-manifolds arise as boundaries of symplectic 4-manifolds, and we are often interested in the filling problem for a given contact 3-manifold.  That is, how many symplectic 4-manifolds have the given contact boundary?  This problem has previously been solved for standard contact structures on lens spaces.  We use

Title: Slice links and smooth 4-manifolds Abstract: We vary the trace embedding lemma in order to prove results about smooth, closed, simply connected 4-manifolds, studying smoothly slice links in them. We focus on homotopy 4-spheres, which are potential counterexamples to the smooth 4-dimensional Poincaré conjecture. In particular, we split them, as for exotic R^4's,  in large and

Title: Infinitely many Lagrangian Tori in Milnor fibers constructed via Lagrangian Fillings of Legendrian links Abstract: One approach to studying symplectic manifolds with contact boundary is to consider Lagrangian submanifolds with Legendrian boundary; in particular, one can study exact Lagrangian fillings of Legendrian links. There are still many open questions on the spaces of exact Lagrangian fillings

Title: The homotopy type of a finite 2-complex with non-minimal Euler characteristic Abstract: Two presentations for a group G which have the same deficiency are called exotic if the corresponding presentation complexes are not homotopy equivalent. The first examples of exotic presentations were found by Dunwoody and Metzler in the 1970s but, owing to the difficulty of

Title: Mutations of reflections and existence of pseudo-acyclic orderings for type An   Abstract: In a recent paper by K.-H. Lee, K. Lee and M. Mills, a mutation of reflections in the universal Coxeter group is defined in association with a mutation of a quiver. A matrix representation of these reflections is determined by a linear ordering

Title: Some Link Detection ResultsAbstract: A central question in low dimensional topology is; how can we distinguish links? In this talk I will discuss various classical invariants which can help us do so, as well as the stronger invariant Knot Floer homology and, time permitting, annular Khovanov homology. Indeed, we will see that these latter

Abstract: Cagri will talk about some symplectic/contact topological aspects of Brieskorn singularities $x^p+y^q+z^r=0$. He’ll tell how to draw the surgery diagrams of their canonical contact structures and prove that the Milnor fiber $M(p,q,r)$ symplectically embeds into $M(p’,q’,r’)$ whenever $p\leq p’$, $q\leq q’$, and $r\leq r’$ by explicitly constructing a Stein cobordism between corresponding canonical contact

Title: Geometry of algebraic surfaces via their Cox rings Abstract: Cox ring is an important tool in modern algebraic geometry and several other branches of mathematics. In the first part of this talk, I will briefly review basic theory of Cox ring and explain how it connects birational geometry and geometric invariant theory. Then I

Title: Geometry of algebraic surfaces via combinatorics of cones Abstract: Effective, nef, semiample cones of projective manifolds are fundamental tools in algebraic geometry. They tell us about the geometry of projective manifolds and there are lots of studies about them. However, we still do not know much about these invariants of projective manifolds of general