Registration is required for all participants of the event and is currently closed. 

Thanks to the financial support of TMD, we will reimburse the transportation costs for a limited number of the graduate and advanced undergraduate students outside of Istanbul.

Program

15:00 - 15:45 Talk 1: Feride Ceren Köse

15:45 - 16:00 Q&A and break 

16:00 - 16:45 Talk 2: İrem Özge Saraç

16:45 - 17:00 Q&A and break

17:00 - 17:45 Talk 3: Hamdi Kayaslan

17:45 - 18:00 Q&A and closing

Feride Ceren Köse - The Jones unknot conjecture and symmetric unions

Abstract: It is still unknown whether there is a nontrivial knot with Jones polynomial equal to that of the unknot. The Jones unknot conjecture asserts that the unknot is indeed the only such knot. The conjecture has been confirmed for several families, including alternating knots and knots with at most 24 crossings. It is in general very hard to even come up with potential candidates that could disprove the conjecture. 

In this talk, we will describe two families of symmetric unions such that if any of these knots were nontrivial, a nontrivial knot with trivial Jones polynomial would exist. Using classical constructions and results in 3-manifold topology, however, we will show that these knots are all trivial and hence these families cannot be used to disprove the Jones unknot conjecture.

İrem Özge Saraç - Compatible relative open books on relative contact pairs via generalized square bridge diagrams

Abstract: Akbulut-Ozbagci and later Arikan gave algorithms both of which construct an explicit compatible open book decomposition on a closed contact 3-manifold which results from a contact (±1)-surgery on a Legendrian link in the standard contact 3-sphere by using square bridge position. 

In this talk, we introduce the “generalized square  bridge position” for a Legendrian link in the standard contact 5-sphere and partially generalize this result to the dimension five via an algorithm which constructs relative open book decompositions on relative contact pairs.