Lars Louder

"It's rather mystifying when you think about songs, where they come from, and, you don't really go to songwriting school, you, you learn by listening to tunes, and then you try to understand them, and take them apart, and see what they're made of, and, you wonder if you can make one too." -- Tom Waits

Associate Professor in the math department at UCL.

LSGNT

I am co-director for first year of the London School of Geometry and Number Theory.

First year students can find their summer reading list here.

Research

Our geometry and topology group.

Groups and geometry in the south east

Papers and preprints

One-relator groups

• Stackings and the W-cycle conjecture (With Henry Wilton.) Canad. Math. Bull. 60 (2017), no.3, 604-612.
• One-relator groups with torsion are coherent (With Henry Wilton.) Math. Res. Lett. 20 (2020) No. 5, 1499-1511
• Negative immersions for one-relator groups (With Henry Wilton.) Duke.
• Uniform negative immersions and the coherence of one-relator groups (With Henry Wilton.)

Limit and free groups

• Krull dimension for limit groups Geometry & Topology 16 (2012) 219-299
• Scott complexity and adjoining roots to finitely generated groups. Groups Geom. Dyn. 7 (2013), no. 2, 451-474
• Simple loop conjecture for limit groups Israel J. Math. 199 (2014), no. 2, 527-545
• Graphs of subgroups of free groups (with D B McReynolds) Algebraic & Geometric Topology 9 (2009) 327-335
• Hyperbolic towers and independent generic sets in the theory of free groups (With Chloé Perin and Rizos Sklinos.) Notre Dame J. Form. Log. 54 (2013), no. 3-4, 521-539
• Magnus pairs in, and free conjugacy separability of, limit groups (With Nicholas Touikan.) N.W.M. Geom Dedicata (2018).

Other groups

• Strong accessibility for finitely presented groups (With Nicholas Touikan.) Geom. Topol. 21 (2017), no. 3, 1805-1835.
• Decision problems, complexity, traces, and representations (With Sean Lawton and Ben McReynolds.) Groups Geom. Dyn. 11 (2017), no.1, 165-188.
• Zariski Closures and Subgroup Separability (With Ben McReynolds and Priyam Patel.) Selecta Math. (N.S.) 23 (2017), no.3, 2019-2027.
• Nielsen equivalence in closed surface groups.

Not groups

• Diameter and spectral gap for planar graphs (With Juan Souto.)
• Three techniques for obtaining algebraic circle packings (With Andrey M. Mishchenko and Juan Souto.) Michigan Math J. Volume 63, Issue 3 (2014), 535-552.

Contact

• Office: 25 Gordon Street, Room 802A
• Email: l dot louder at ucl.ac.uk
• Personal email: pick something then at d503.net