This is a weekly series of lectures by distinguished visitors and Penn State research faculty. These lectures are instrumental in focusing the interest of PMASS participants on various research areas both during their participation in the program and in their future selection of graduate programs.

## 2014

Neural networks and labeled trees

Manfred Denker, Penn StateCoverings by systems of linear equations

Mihran Paikian, Penn StateBilliard table as mathematician's playground

Anatole Katok, Penn StateProbability puzzles

Victoria Sadovskaya, Penn StateCan you hear the shape of the drum?

Vadim Kaloshin, University of Maryland, College ParkGrouping and rearranging terms in infinite series

Joe Roberts, Penn StateWhat is a random number?

Jason Rute, Penn State

## 2013

A short history of length

Joel C. Langer, Case Western Reserve UniversityPrime number theorem

Andrey Gogolev, Binghamton UniversityBezout's theorem

Karl Schwede, Penn StateGeometry and arithmetic of Apollonian gasket

Alexandre Kirillov, University of PennsylvaniaFractals and dimension

Victoria Sadovskaya, Penn StateProofs from the Book

Sergei Tabachnikov, Penn StateGame Theory 101: numerical modeling of life events

Eii Byrne, Penn State

## 2012

The first digit

Amie Wilkinson, University of ChicagoCommutative and Noncommutative Symmetric Functions

Vladimir Retakh, Rutgers UniversityBeing right more often can make you more wrong

John Roe, The Pennsylvania State UniversityPhysical discoveries and proofs of mathematical theorems

Mark Levi, The Pennsylvania State UniversityLake fish population estimates and mixing properties

Jana Rodriguez Hertz, IMERL, UruguayThe Continuum Hypothesis

Jan Reimann, The Pennsylvania State UniversityThe Navier-Stokes equations

Eugene Wayne, Boston University

## 2011

Morleyâ€™s theorem

John Roe, The Pennsylvania State UniversityRamanujan, Fibonacci numbers, and continued fractions

George Andrews, The Pennsylvania State UniversityEquiareal dissections

Sergei Tabachnikov, The Pennsylvania State UniversityBilliard table as a mathematician's playground

Anatole Katok, The Pennsylvania State UniversityTheorems of Poncelet and Marden -- two of the most beautiful theorems

Vladimir Dragovic, MI SANU Belgrade/ GFM, University of LisbonThe bigness of things

Vaughn Climenhaga, University of Maryland visiting the Pennsylvania State UniversitySymbolic dynamics

Omri Sarig, The Pennsylvania State University