06 July 2020, 18:30 - (UTC+3)

Title : Foams and Surface Braids as Higher Categories and Generalizations

Speaker : Scott Carter

Organization : Knots and representation theory


Five Categorical Principles are articulated: (1) Different things are not equal. (2) Arrows are used to compare things. (3) Doing followed by un-doing may, or may not, be the same as not doing. (4) Simultaneity is illusory, (5) Change followed by exchange is comparable to exchange followed by change. Then starting from a modification of algebraic axioms (multiplication, comultiplication, (co)associativity,  and pairing) embedded foams are formulated as quadruple arrows in a certain multi-category. Briefly, quintuple arrows will be discussed in this context, and then we'll move to surface braids, braided 3-manifolds and illustrate a few braided 4-manifolds.

08 July 2020, 10:30 - (UTC+3)

Title : The strong homotopy fusion number of ribbon knots
Speaker :  Sungkyung Kang (IMS, CUHK)

Organization : Moscow-Beijing topology seminar (by Zoom)


The fusion number of a ribbon knot K is the minimal number of 1-handles needed to construct a ribbon disk for K. The strong homotopy fusion number of a ribbon knot K is the minimal number of 2-handles in a handle decomposition of a ribbon disk complement. The strong homotopy fusion number is a lower bound for the fusion number. We give examples of ribbon knots with strong homotopy fusion number one and arbitrarily large fusion number. Our main tools are Juhasz-Miller-Zemke’s bound on fusion number coming from the torsion order of knot Floer homology and Hanselman-Watson’s cabling formula for immersed curves.

The seminar will be held during 15:30--17:00 (Beijing time) on Zoom.

Meeting ID: 831 5020 0580

Password: 141592

09 July 2020, 15:30 - (UTC+3)

Title : Чем фундаментальная группа бутылки Клейна отличается от всех остальных групп поверхностей?
Speaker :  Клячко А. А.

Organization : Математический коллоквиум


Теорема Мажуги говорит, что фундаментальная группа $H$ любой связной поверхности, кроме, быть может, бутылки Клейна, является ретрактом всякой конечно порождённой группы, содержащей $H$ в качестве вербально замкнутой подгруппы. Я расскажу об этой теореме и о других подобных фактах, а также о том, что происходит с бутылкой Клейна в действительности.

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Meeting ID: 833 9984 9040

Password: 990340

Time line

Chicago -8h

Moscow +0h

Beijing +5h

Seoul +6h

Tokyo +6h

Kim, Seongjeong,

e-mail :ksj19891120@gmail.com