# CS 2014: Invited speakers

**Maxim Kontsevich**

Maxim is a math professor at the Institut des Hautes Études Scientifiques, France. He received the Henri Poincaré Prize in 1997, the Fields Medal in 1998, the Crafoord Prize in 2008, the Shaw Prize and Fundamental Physics Prize in 2012, the Breakthrough Prize in Mathematics in 2014. His work concentrates on geometric aspects of mathematical physics, most notably on knot theory, quantization, and mirror symmetry.

*Tropical algebra and geometry*

In tropical algebra one can add and multiply numbers, but the subtraction is forbidden. Also one has a strange rule A+A=A for any A. I will explain how to use tropical algebra for algberaic equations on usual nontropical numbers with very large or very small coefficients. Tropical curves given by a tropical equation are bizarre spiderweb-like figures. Even the usual line X+Y=1 became a three-legged creature. I will explain how to draw tropical curves, and how they are related to complex numbers.

**Moira Chas **

Moira is currently an Assistant Professor at StonyBrookUniversity. She received her in Ph.D. Universitat Autònoma de Barcelona, Spain. Her research focuses on Low Dimensional Topology, specifically understanding and exploring the wonderful universes left to us by Poincare and Thurston. She designs mathematical experiments and implements these experiments often jointly with Stony Brook Undergraduate students.She believes that mathematical thinking is a powerful tool and tries her best to transmit this tool to all students she finds on her way.

*Symmetries in Math*

Symmetries appear in many forms in our world. We can find them in beehive, in an orange, in our own human shape. Mirrors create fantastic symmetries and symmetry is part of the essence of many art works. We walk daily over symmetric tiles and often eat food that has some form of symmetry. In this hour, I’ll discuss symmetries from a mathematical point of view. A mathematician looks at symmetries and finds ways to classify them and produce a list of symmetries that satisfy certain conditions. For instance, there are exactly 17 types of symmetries in standard wallpapers (there are of course an infinity of patterns, but exactly 17 ways of repeating them on the wall). I’ll discuss each of these types of symmetries and try to explain why there are only 17.

**Dennis Sullivan**

Dennis holds the Albert Einstein Chair at the City University of New York Graduate Center, and is a professor at StonyBrookUniversity. Awards include the Oswald Veblen Prize in Geometry; the Prix Élie Cartan of the French Academy of Sciences; the King Faisal International Prize for Science i National Medal of Science; AMS Steele Prize for Lifetime Achievement and the Wolf Prize in Mathematics in 2010 for "his contributions to algebraic topology and conformal dynamics". In 2012 he became a fellow of the American Mathematical Society.

*Pictures of fractions*

If you watch old western movies the wagon wheels are turning and turning and at some point they seem to be reversing directions.there is a picture about fractions which can explain this. What do you think the picture of the fraction 2/5 is? It is a five pointed start which is traced out in the clockwise direction. And the picture of the fraction 3/5 is the same five pointed start traced out in the opposite direction. These pictures of fractions are examples of mathematical ideas called circular ordering of points, or more generally, the orbits of a dynamical system. Another example of orbit of a dynamical system is an interesting curve generated by a famous mathematician Bill Thurston and I will discuss how this curve can be viewed as a dynamical system. These two discussions are united by a third discussion called continued fractions.

** Hobbie Lawrence**

Lawrence is currently Proffesor and Chair Biology at AdelphiUniversity, he received his Ph.D. at MIT His research is in plant molecular genetics, the molecular mechanism of action and oftransport of the plant hormone auxin and the role of auxin in plant physiology and development.

*Genetically-modified crops: Frankenfoods or panacea?*

In this lecture, Dr. Lawrence Hobbie will discuss the science behind genetically-modified crop plants: how the genetic modification happens, what kinds of genetically-modified crops currently exist and are being developed, and why these plants are controversial.