**CUNY Graduate Center**

**Room 6417**

**Fridays 2:00pm-3:30pm**

**Organized by Russell Miller, Alice Medvedev and Roman Kossak**

**Calendar**

**December 6**

**Chris Laskowski**,
University of Maryland

**TBA**

**Abstract**

**November 29**

**Seminar cancelled**

Thanksgiving break.

**November 22**

**Alex Kruckman**,
Wesleyan University

**TBA**

**Abstract**

**November 15**

**Sandra Müller**,
University of Vienna

**TBA**

**Abstract**

**October 25**

**Jouko Väänänen**,
University of Helsinki

**TBA**

**Abstract**

**October 11**

**Miha Habič**,
Bard College

**TBA**

**Abstract**

**October 4**

**Hans Schoutens**,
CUNY

**All your favorite Taylor series wrapped up in a nice little package: the ring of 'catanomials'.**

**Abstract**

The nice little package is a regular, existentially closed, Henselian local subring of the ring of (formal) power series over your favorite field (R, C, Q?). Moreover, this ring is closed under derivations, anti-derivations, composition, etc. The favorite series (in a single variable, say) include all algebraic functions, all elementary functions, all hypergeometrical functions, all holonomic functions (i.e., solutions of a linear, algebraic ODE), etc.

The way to obtain these is by looking at some non-standard model of the theory of polynomial rings, and then defining its 'catanomials' as the truncations of these functions by only looking at its finite degree terms. In the special case that the non-standard model is an ultrapower of the polynomial ring, the resulting algebra, called the catapower, is just the full power series ring. Whereas the latter may sound less glorious, we can nonetheless do better by taking different non-standard models. Enters the embedded model of PA* of such a model and its standard systems!

**September 27**

**Alf Dolich**,
CUNY

**TBA**

**Abstract**

**September 20**

**Artem Chernikov**,
UCLA

**N-dependent groups and fields**

**Abstract**

A first-order theory is n-dependent if the edge relation of an infinite generic (n+1)-hypergraph is not definable in any of its models. N-dependence is a strict hierarchy increasing with n, with 1-dependence corresponding to the well-studied class of NIP theories. I will discuss recent joint work with Nadja Hempel on trying to understand which algebraic structures are n-dependent.

**September 13**

**Seminar cancelled**

**September 6**

**Russell Miller**,
CUNY

**A computability-theoretic proof of Lusin's Theorem**

**Abstract**

Lusin's Theorem, from real analysis, states that for every Borel-measurable function $f$ from $\mathbb R$ to $\mathbb R$, and for every $\epsilon > 0$, there exists a continuous function $g$ on $\mathbb R$ such that $\{ x\in\mathbb R~:~f(x) \neq g(x)\}$ has measure $< \epsilon$. This is proven in most introductory real analysis courses, but here we will give a proof using computability theory and computable analysis. In addition to the theorem itself, the proof will establish an effective way of producing $g$ from $f$ and $\epsilon$, and will pick out, for each $f$, the specific set of troublemakers $x$ in $\mathbb R$ that create all the discontinuities.

**August 30**

**Seminar cancelled**

**Previous Semesters**