Date |
Speaker |
Title |

Oct 28 | Samuel Tripp,
Dartmouth College |
TBA |

Oct 21 | Zachary Winkeler,
Dartmouth College |
TBA |

Oct 14 | Daniel Alvarez-Gavela,
MIT |
TBA |

Oct 7 | Misha Tyomkin,
Dartmouth College |
Various facets of torsion theory: Whitehead, Reidemeister and Milnor |

Sept 30 | Misha Tyomkin,
Dartmouth College |
Numbers on barcode of a strong Morse function |

Sept 23 | Emanuele Zappala,
University of Tartu, Estonia |
Cocycle invariants of knots and knotted surfaces |

Sept 16 | Sergey Maksimenko Corresponding member of the National Academy of Science of Ukraine, President of the Kiev Mathematical Society, Institute of mathematics of NAS of Ukraine, Kyiv, Ukraine |
Combinatorial symplectic symmetries of smooth functions on surfaces |

**Abstracts**

#### October 28, 2021: Samuel Tripp "TBA"

*Abstract:*

#### October 21, 2021: Zachary Winkeler "TBA"

*Abstract:*

#### October 14, 2021: Daniel Alvarez-Gavela "TBA"

*Abstract:*

#### October 7, 2021: Misha Tyomkin "Various facets of torsion theory: Whitehead, Reidemeister and Milnor"

*Abstract:*

#### September 30, 2021: Misha Tyomkin "Numbers on barcode of a strong Morse function"

*Abstract:*

#### September 23, 2021: Emanuele Zappala "Cocycle invariants of knots and knotted surfaces "

*Abstract:* In this talk I will introduce the notions of racks and quandles,
as well as their cohomology. I will discuss the diagrammatic interpretation
of these algebraic structures, and show how to use this to construct a
partition function that is an invariant of Reidemeister moves. Using the
same principles, I will also show that it is possible to obtain an invariant
of knotted surfaces in 4-space, defining certain partition functions based
on quandle 3-cocycles. These results were introduced in Trans. Amer.
Math. Soc. 355 (2003) 3947-3989 by Carter, Jelsovsky, Kamada, Langford
and Saito. Then, I will discuss how to generalize the previous results by means
of ternary quandle cohomology to get invariants of framed links and compact
oriented surfaces with boundary (embedded in 3-space). I will present
applications of all these invariants throughout the talk, including a generalization
of the cocycle invariants to quantum invariants.

#### September 16, 2021: Sergey Maksimenko "Combinatorial symplectic symmetries of smooth functions on surfaces "

*Abstract:*
Let M be a compact orientable surface equipped with a symplectic form w, P be either the real line of the circle, and f:M→P a smooth function.
Let also S(f,w) = {h ∈ Diff(M) | foh=f and h^{*}w=w} be the group of diffeomorphisms of M which mutually preserve f and w, and p:S(f,w)→π_{0}S(f,w) be the natural projection into the group π_{0}S(f,w) of path components of S(f,w).
It is shown that for a large class of smooth maps f:M→P, which includes all Morse maps, the homomorphism p admits a section homomorphism s: π_{0}S(f,w)→S(f,w).
In other words, in each isotopy class γ of diffeomorphisms mutually preserving f and w one can choose a representative h_{γ} ∈ S(f,w) so that the collection {h_{γ}}_{γ} constitute a subgroup of S(f,w), i.e. h_{γ}h_{γ'} = h_{γ γ'}.
A variant of such result for non-orientable surfaces is also given.
As an application it is also shown that every finite group is a subgroup of S(f,w) for some M, f and w.