Wie halte ich einen guten Seminarvortrag? (von Prof. Manfred Lehn)

Knot theory has transformed over the years from a specialised branch of topology to a very popular area of study in mathematics. In the early 20th century, topologists studied knots from the point of view of knot groups and invariants from homology. More recently, many breakthrough results about knot theory established its connection with physics, algebraic geometry, quantum theory etc.

The goal of this seminar is to have a basic understanding of knot theory, and then to study the special knots in contact manifolds called Legendrian and transverse, respectively. No prior knowledge of contact geometry will be assumed.

Vorträge (Talks will be in English):

11.10.22	Introduction to smooth knot theory I [R 1, 3C], [A 3] (definition, knot equivalence, isotopy, knot diagrams, mirrors, knot invariants, the unknot and torus knots) Rima Chatterjee
18.10.22	Introduction to smooth knot theory II [R 5 A, D], [A 1.2, 1.3, 4] (genus, Seifert's algorithm, connected sum, prime vs non-prime knots, linking number, Reidemeister moves) Rima Chatterjee
25.10.22	Introduction to smooth knot theory III [R 3 A, B, D], [A 9] (the knot group, knot complement and homology, Wirtinger presentation trefoil is not the unknot) Humay Khalilova
1.11.22	no seminar
8.11.22	Introduction to contact topology and Legendrian and transverse knots [G 2.1, 3.1, 3.2], [E 2.1 - 2.4] Ilona Schlömer
15.11.22	Classical invariants of Legendrian and transverse knots [G 3.5], [E 2.5 - 2.7] Fabian Bühner
22.11.22	Introduction to convex surfaces [G 4.8], [E 2.8] Norman Thies
29.11.22	Tight vs overtwisted, and Bennnequin inequality [E 2.9, 3], [G 4.5, 4.6.5] Tilman Becker
6.12.22	Classification of Legendrian and transverse knots [EH] Rima Chatterjee
	There is the option for three more talks in January

Literatur:

[A]	C. Adams: The Knot Book, Freeman, 1994.
[E]	J. B. Etnyre: Legendrian and transversal knots, Handbook of Knot Theory, Elsevier, 2005.
[EH]	J. B. Etnyre, K. Honda: Knots and contact geometry I - Torus knots and the figure eight knot, J. Symplectic Geom. 1 (2001), 63-120.
[G]	H. Geiges: An Introduction to Contact Topology, Cambridge University Press, 2008.
[PS]	V. V. Prasolov, A. B. Sossinsky: Knots, Links, Braids and 3-Manifolds, American Mathematical Society, 1997.
[R]	D. Rolfsen: Knots and Links, Publish or Perish, 1990.

H. Geiges, 24.5.22