The Part III Seminars took place on **Wednesday 28th November** in the afternoon, and** Thursday 29th, Friday 30th November** all day. They were organised by Julia Goedecke (DPMMS) and Toby Wood (DAMTP).

Thanks to everyone who gave talks, and to all the group leaders! It was a very successful event.

Talks were 30 minutes, plus 15 minutes questions.

**Category Theory **- Group Leaders: **Nathan Bowler and Marie Bjerrum***These talks took place on Wednesday afternoon in MR15.*

Abstracts

2:00 - 2:45 Andrew Swan (aws31) - What is a Category?

2:45 - 3:30 John Harvey (jh600) - Universal Properties: The Tensor Product (and friends!)

3:30 - 4:15 Roko Mijic (rm382) - An introduction to Operads

4:30 - 5:15 Sam van Gool (sjv25) - The Eilenberg-Moore Category

5:15 - 6:00 Philipp Schaefer (pms51) - An Adjunction between Sets and Groups

**Algebraic Topology** - Group Leader: **Charles Vial ***These talks took place on Thursday in MR11 (?) and MR13.*

Abstracts

9:45 - 10:30

10:30 - 11:15

The remaining talks will be in

2:00 - 2:45 Adam Mole (am619) - The excision theorem in singular homology

2:45 - 3:30 Philipp Freeman (paf31) - Brown representability theorem

3:30 - 4:15 Maurice Chiodo (mcc56) - Braids and knots

4:30 - 5:15 Sam Gunningham (stpg2) - links between homotopy and homology

**Algebraic Geometry** - Group Leader: **Julian Holstein**

Abstracts

9:45 - 10:30 - David Holmes (dsth3) - There is too much maths - let's destroy some!

10:30 - 11:15 - Alexander Shannon (adjs2) - What is a stack and why do we care?

14:00 - 14:45

14:45 - 15:30 - Jack Thorne (jat58) - Compactness in the category of algebraic varieties

15:30 - 16:15 - Mariano Zeron-Medina (mz276) - Covering spaces and the fundamental group

16:30 - 17:15 - Will Merry (wjm29) - Coalgebras and algebraic geometry

17:15 - 18:00 - Michael Magee (mrm40) - Realizability of smooth compact manifolds by moduli spaces of planar linkages

**Differential Geometry **- Group Leader: **Jonny Evans***These talks took place on Thursday afternoon in MR5.*Abstracts

09:45 - 10:30

14:00 - 14:45 - Dominic Jänichen (dgj24) - Huygens' principle and Contact geometry

14:45 - 15:30 - Spiros Adams-Florou (sta25) - A Proof of De Rham's Theorem using induction on open sets

15:30 - 16:15 - Rune Haugseng (rgh36) - The Hodge Decomposition Theorem

16:30 - 17:00 - Richard Harris (rmh49) - Introduction to Morse Theory

17:15 - 18:00 - Alex Ellis (ape21) - Unoriented Cobordism

**Number Theory **- Group Leaders: **Ant Lei** and **Alex Chmelnitzki***These talks took place on Friday morning in MR14 and Friday afternoon in MR13.*

Abstracts

10.30 - 11.15

11.30 - 12.15

12.15 - 13.00

14.45 - 15.30

15.30 - 16.15

16.30 - 17.15

**Algebra** - Group Leader: **James Griffin***These talks took place on Thursday afternoon in MR4.*

Abstracts

12:15 - 13:00

14:00 - 14:45

14:45 - 15:30

15:30 - 16:15

16:30 - 17:15

**Combinatorics **- Group Leader: **Vicky Neale***These talks took place on Friday morning in MR12 and MR15.*

Abstracts

09:45 - 10:30

10:30 - 11:15

11:30 - 12:15

**Analysis** - Group Leader: **Alexander Lorz***These talks took place on Wednesday afternoon in MR11.*

Abstracts

2:00-2:45 David Fidler (drf36) - A subset of the plane intersecting every line in exactly 2 points?

2:45-3:30 Sebastian Helmensdorfer (stwh2) - Eigenvalues of Jacobi Matrices

3:30-4:15 Emil Wiedemann (efw24) - The Dirichlet Problem and Brownian Motion

**Statistics / Probability / Finance **- Group Leader:** Sarah Lilienthal***These talks took place on Friday in MR9 and MR3.*

Abstracts

09:45 - 10:30

10:30 - 11:15

11:30 - 12:15

12:15 - 13:00

14:00 - 14:45

14:45 - 15:30

**Fluids** - Group Leader: **Rosie Robison***These talks took place on Thursday afternoon in*

Abstracts

15:30 - 16:15 José Cardesa-Duenas (jic27) - Topological study of electromagnetically forced 2D laminar flows

16:30 - 17:15 Tom Flannaghan (tjf37) - Taylor Columns

17:15 - 18:00 Sam Pegler (ssp23) - The Wave-Driven Cooling of the Upper Summer Mesosphere and Noctilucent Clouds

**Physics I (HEP)** - Group Leader: **Matt Dolan***These talks took place on Thursday in MR3.*

Abstracts

09:45 - 10:30 Mahdi Godazgar (mmg31)- The Petrov Classification

10:30 - 11:15 Charles Strickland-Constable (cs433) - SL(2,C) and the Lorentz Group

11:30 - 12:15 Hadi Godazgar (hmg30) - The diagramatic expression for Green's function

12:15 - 13:00 Tae-Joon Cho (tc262) - Diagrammatica: A derivation of Feynman diagrams.

**Physics II (QFT/GR)** - Group Leader: **Jon Middleton***These talks took place on Friday in MR4.*

Abstracts

14:00 - 14:45

14:45 - 15:30

15:30 - 16:15

16:30 - 17:15