### Upcoming Talks

#### Zahlentheoretisches Kolloquium

**Title:**The number of prime factors of integers - classical results and recent variations of the classical theme

**Speaker:**Dr. Krishnaswami Alladi (University of Florida)

**Date:**15.03.2024, 15:00 Uhr

**Room:**Seminarraum Analysis-Zahlentheorie, Kopernikusgasse 24, 2.OG

**Abstract:**

Although prime numbers have been studied

since Greek antiquity, the first systematic study of the

number of prime factors is due to Hardy and Ramanujan

in 1917. Subsequently, with the work of Paul Turan, Paul

Erdos, and Marc Kac, the subject of Probabilistic Number

Theory was born around 1940 and has blossomed

considerably since then. We shall discuss classical

work on the number of prime factors of integers and more

recent results of ours with restrictions on the size of the

prime factors, that lead to very interesting variations of

the classical theme. My most recent results are jointly

with my former PhD student Todd Molnar. A variety of

techniques come into play - the classical Perron integral

approach, an analytic method of Atle Selberg, the behavior

of solutions to certain difference - differential equations,

and the Buchstab-de Bruijn iteration. The talk will be

accessible to non-experts.

#### Combinatorics Seminar

**Title:**Ramsey problems for monotone (powers of) paths in graphs and hypergraphs

**Speaker:**Lior Gishboliner (ETH Zurich)

**Date:**Friday 8th March 12:30

**Room:**Online meeting (Webex)

**Abstract:**

The study of ordered Ramsey numbers of monotone paths for graphs and hypergraphs has a long history, going back to the celebrated work by Erdos and Szekeres in the early days of Ramsey theory. We obtain several results in this area, establishing two conjectures of Mubayi and Suk. This talk is based on a joint work with Zhihan Jin and Benny Sudakov.

Meeting link:

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#### Combinatorics Seminar

**Title:**Semirestricted Rock, Paper, Scissors

**Speaker:**Svante Janson (Uppsala University)

**Date:**Friday 1st March 12:30

**Room:**AE06, Steyrergasse 30

**Abstract:**

A semirestricted variant of the well-known game Rock, Paper, Scissors was recently studied by Spiro et al (Electronic J. Comb. 30 (2023), #P4.32). They assume that two players $R$ (restricted) and $N$ (normal) agree to play $3n$ rounds, where $R$ is restricted to use each of the three choices exactly $n$ times each, while $N$ can choose freely. Obviously, this gives an advantage to $N$. How large is the advantage?

The main result of Spiro et al is that the optimal strategy for $R$ is the greedy strategy, playing each round as if it were the last. (I will not give the proof, and I cannot improve on this.) They also show that with optimal play, the expected net score of $N$ is $\Theta(\sqrt{n})$. In the talk, I will show that with optimal play, the game can be regarded as a twice stopped random walk, and I will show that the expected score is asymptotic to $c \sqrt{n}$, where $c = 3\sqrt{3}/(2\sqrt{\pi}})$.