Organizing Committee

• Huijun Fan (SMS PKU)
  symplectic geometry and mathematical physics, geometric analysis
• Sergey Gorchinskiy (MI RAS)
  algebra and geometry: algebraic geometry, K-theory
• Hailiang Li (SMS CNU)
  fluid mechanics, partial differential equations, analysis
• Jinsong Liu (AMSS)
  algebraic geometry: singularity theory
• Yi Liu (BICMR)
  Topology of 3-manifolds, hyperbolic geometry
• Denis Osipov (MI RAS)
  algebraic geometry, number theory, integrable system
• Ye Tian (UCAS, AMSS)
  Number Theory, Arithmetic Geometry, Iwasawa Theory
• Alexey Tuzhilin (MSU)
  geometry: Riemannian and metric geometry
• Yue Yang (CE PKU)
  computation mathematics and mechanics
• Ping Zhang (AMSS)
  P. D. E.: fluid equation and semi-classical analysis
• Alexander Zheglov (MSU)
  geometry: algebraic geometry, integrable system

PROGRAM

	Lei Chen University of Maryland
Bio: Lei Chen graduated from University of Chicago and did her Postdoc at Caltech. She then joined University of Maryland in 2021. Her research area is in geometric topology, in particular mapping class group and homeomorphism groups.

Mapping class groups of circle bundles over a surface.

In this talk, we study the algebraic structure of mapping class group Mod(M) of 3-manifolds M that fiber as a circle bundle over a surface. We prove an exact sequence, relate this to the Birman exact sequence, and determine when this sequence splits. We will also discuss the Nielsen realization problem for such manifolds and give a partial answer. This is joint work with Bena Tshishiku and Alina Beaini.

Sergey Melikhov MI RAS

Bio: Sergey Melikhov is a senior researcher at the Steklov Mathematical Institute. He graduated from Lomonosov Moscow State University (2001) and obtained a k.f.m-n. (PhD) degree from the Steklov Institute (2004) and another PhD degree from University of Florida (2005), with no overlap in content between the two dissertations. Received the Moebuis Contest Prize of the Independent University of Moscow (2000) and Russian Academy of Sciences Medal for Young Scientists (2006). Held visiting positions at the University of Tennessee (2007/08), Dartmouth College (2012) and Institute for Advanced Study (2013). Research interests include geometric topology (links modulo knots, embedding theory, combinatorial topology), algebraic topology of metrizable spaces (shape theory and axiomatic homology), foundations of mathematics (extensions of intuitionistic logic, meta-logics, constructive type theories).

Is every knot isotopic to the unknot?

50 years ago D. Rolfsen asked two questions: (A) Is every knot in the 3-sphere isotopic (=homotopic through embeddings) to a PL knot (or, equivalently, to the unknot)? In particular, is the Bing sling isotopic to a PL (=piecewise linear) knot? (B) If two PL links in the 3-sphere are isotopic, are they PL isotopic?

We show that the answer to (B) is positive if finite type invariants separate links in the 3-sphere. [arXiv:2406.09331]

Regarding (A), it was previously shown by the author that not every link in the 3-sphere is isotopic to a PL link [arXiv:2011.01409]. Now we show that the Bing sling is not isotopic to any PL knot by an isotopy which extends to an isotopy of 2-component links with linking number 1. Moreover, the additional component may be allowed to self-intersect, and even to get replaced by a new one as long as it represents the same conjugacy class in G/[G',G''], where G is the fundamental group of the complement to the original component. [arXiv:2406.09365]

The proofs are based in part on a formula explaining the geometric meaning of the formal analogues of Cochran's derived invariants for PL links of linking number 1. These formal analogues are defined by using the 2-variable Conway polynomial. [arXiv:math/0312007]

 The meeting will be held in the form of a webinar on the Voov platform.

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