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Anna Parlak

I am currently a second year PhD student exploring the geometry and topology of 3-manifolds under the supervision of Dr Saul Schleimer.

You can get in contact with me via add.


In the academic year 2018/2019 I am responsible for the geometry & topology reading seminar. In term 1 we're reading Geometry of the mapping class groups I: Boundary amenability by Ursula Hamenstädt. The meetings happen on Fridays* at 10 am in B1.01.

*possibly exluding 26/10 and 30/11, when the GGSE meetings are scheduled.


A BIT OF HISTORY

Before coming to Warwick, I obtained BSc and MSc degrees in mathematics from the University of Gdańsk, Poland.

My mathematical interests were centred around mapping class groups.

The aim of my master’s thesis was to investigate the existence and possible degrees of roots of Dehn twists, crosscap slides and crosscap transpositions in the mapping class groups of closed nonorientable surfaces. (It is known that a finite number of Dehn twists and a single crosscap slide or a crosscap transposition generate the whole group).

This was mainly a generalisation/extension of the results previously obtained by Margalit & Schleimer, McCullough & Rajeevsarathy and Monden in the orientable case.

The content of my master’s thesis is summarised in the following two papers, written jointly with my former supervisor Michał Stukow.

  1. A. Parlak, M. Stukow. Roots of crosscap slides and crosscap transpositions.
    Periodica Mathematica Hungarica (2017), Vol. 75, Issue 2, pp 413 – 419.
    arXiv:1601.06096 [math.GT]
  2. A. Parlak, M. Stukow. Roots of Dehn twists on nonorientable surfaces.
    arXiv:1701.00531 [math.GT]


My bachelor's thesis concerned simple knot invariants.

I also have a BSc degree in biotechnology.

Over the last few years I took part in several conferences and workshops which are listed here.

I also gave some talks:
  1. Junior Geometry and Topology Seminar, University of Warwick; Coventry, UK, 22 January 2018.
    Roots of Dehn twists
  2. Young Topologists Meeting 2017; Stockholm, Sweden, July 2017.
    Roots in the mapping class group of a nonorientable surface
  3. The 19th International Workshop for Young Mathematicians - Algebraic Geometry; Kraków, Poland, September 2016.
    Automorphisms Groups of Hyperelliptic Riemann Surfaces
  4. XIII Workshop for Mathematical Students' Associations; Hel, Poland, May 2016.
    Classification of finite subgroups of the mapping class group of a punctured sphere
  5. 18th Andrzej Jankowski Memorial Lecture Mini Conference; Gdańsk, Poland, May 2016.
    Roots of crosscap slides and crosscap transpositions
  6. The 18th International Workshop for Young Mathematicians - Algebraic and Differential Topology; Kraków, Poland, September 2015.
    Some Remarks on Quandles and Their Applications

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