DMS Colloquium: Dr. Dana Bartošová

Speaker: Dana Bartošová, University of Florida 

Title: Model Theory in Ramsey Theory

Abstract: Classical finite Ramsey theorem states that for any natural number \(m\leq n\) and a number of colours \(k\geq 2\), there is a natural number \(N\) such that whenever we colour \(m\)-tuples of \(\{1,2,\ldots, N\}\) by \(k\) colours, there is an \(n\)-element subset \(Y\) of  \(\{1,2,\ldots, N\}\) whose all \(m\)-element subsets received the same colour. This theorem has generalizations in possibly every area of mathematics. In this talk, we will focus on structural Ramsey theory, which in place of finite sets speaks about finite structures in some first-order language, such as finite graphs, finite Boolean algebras, or finite vector spaces over finite fields. I will talk about recent research in model-theoretic transfer principles of Ramsey properties between classes of finite structure (joint work with Lynn Scow) and from classes of finite structures to their ultraproducts (AIMSQuaREs project with Mirna Dzamonja, Rehana Patel, and Lynn Scow).

Faculty host: Joseph Briggs

Short Bio: Dana Bartosova obtained her undergraduate and master’s degree from the Charles University in Prague, as well as a master’s degree from the Free University of Amsterdam. She went on to complete her Ph.D. at the University of Toronto in 2013. Dana had postdocs at a semester program at HIM institute in Bonn, University of Sao Paulo, and Carnegie-Mellon University, and since 2018, she has been an assistant professor at the University of Florida. Her research is supported by an individual NSF grant and an NSF CAREER grant. She is also the co-founder of Math Parents Coffee and the director of UF Math Circle.