Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, January 21, 2020.

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Tuesday, January 21, 2020

1:00 pm in 241 Altgeld Hall,Tuesday, January 21, 2020

Organizational meeting

Abstract: Just a short organizational meeting for Logic seminar and the MT/DST Seminar.

2:00 pm in 243 Altgeld Hall,Tuesday, January 21, 2020

Lichiardopol's Conjecture on Disjoint Cycles in Tournaments

Douglas B. West (Zhejiang Normal University and University of Illinois)

Abstract: In a 1981 survey on cycles in digraphs, Bermond and Thomassen conjectured that every digraph with minimum outdegree at least $2k-1$ contains $k$ disjoint cycles. In 2010, Lichiardopol conjectured a stronger property for tournaments: for positive integers $k$ and $q$ with $q\ge3$, every tournament with minimum out-degree at least $(q-1)k-1$ contains $k$ disjoint cycles of length $q$.

Bang-Jensen, Bessy, and Thomassé [2014] proved the special case of the Bermond--Thomassen Conjecture for tournaments. This implies the case $q=3$ of Lichiardopol's Conjecture. The case $q=4$ was proved in a masters thesis by S. Zhu [2019]. We give a uniform proof for $q\ge5$, thus completing the proof of Lichiardopol's Conjecture. This result is joint work with Fuhong Ma and Jin Yan of Shandong University.

4:00 pm in 245 Altgeld Hall,Tuesday, January 21, 2020

The Helly geometry of some Garside and Artin groups

Jingyin Huang   [email] (Ohio State University)

Abstract: Artin groups emerged from the study of braid groups and complex hyperplane arrangements, and they are connected to Coxeter groups, 3-manifold groups, buildings and many others. Artin groups have very simple presentation, yet rather mysterious geometry with many basic questions widely open. I will present a way of understanding certain Artin groups and Garside groups by building geometric models on which they act. These geometric models are non-positively curved in an appropriate sense, and such curvature structure yields several new results on the algorithmic, topological and geometric aspects of these groups. No previous knowledge on Artin groups or Garside groups is required. This is joint work with D. Osajda.