Anna Erschler facts for kids

Anna Gennadievna Erschler, born on February 14, 1977, is a talented Russian mathematician who now works in France. She is an expert in areas of math called geometric group theory and probability theory. She especially studies how things move randomly, like a "random walk" on groups of numbers or shapes.

Anna Erschler's Journey in Math

Anna Erschler started her math studies in 1994 at Saint Petersburg State University. She earned her first advanced degree, a Master of Science (M.Sc.), in 1999. She also spent a year studying at Tel Aviv University in 1999-2000.

In 2001, she completed her Ph.D. (a very high-level degree in research) at Saint Petersburg State University. Her Ph.D. advisor was Anatoly Vershik, and her research was about the "geometric and probabilistic properties of wreath products." Later, in October 2012, she earned another important degree called a habilitation from the University of Paris 11. This degree allows her to supervise other Ph.D. students.

Her Work as a Researcher

After getting her Ph.D., Anna Erschler worked as a postdoc (a temporary research position) at the Steklov Institute in Saint Petersburg (2001-2002) and at the Institut des Hautes Études Scientifiques in Paris (2002-2003).

From 2003, she joined the Centre national de la recherche scientifique (CNRS), which is a big research organization in France. She worked at the University of Lille and then at the University of Paris 11. She started as a "Chargée de recherche" (researcher) and then became a "Directrice de recherche" (research director) in October 2013. Since May 2014, she has been a research director at CNRS, DMA/ENS, Orsay.

She also helps edit an important math magazine called Groups, Geometry and Dynamics.

What Anna Erschler Studies

Anna Erschler's work helps us understand complex mathematical ideas. For example, she showed that certain shapes in math, called "asymptotic cones" of a hyperbolic space, always look like "real trees" (which are like branching structures). She proved that this special property is what makes a space "hyperbolic."

She also did important research on something called the "drift" of a random walk. Imagine a tiny particle moving randomly on a map of a group of numbers or shapes (called a Cayley graph). Anna Erschler figures out how far this particle will likely be from its starting point after a certain number of steps. Her work has shown new and surprising ways these random walks can behave.

Awards and Honors

Anna Erschler has received many awards for her amazing work in mathematics:

• In 2001, she won the Möbius Prize from the Independent University of Moscow.
• In 2002, she received the Annual Prize of the Saint Petersburg Mathematical Society.
• In 2010, she was invited to speak at the International Congress of Mathematicians in Hyderabad. This is a very big honor in the math world! She talked about "Poisson–Furstenberg boundaries, large-scale geometry and growth of groups."
• In the summer of 2010, she was the ninth Emmy Noether visiting professor at the University of Göttingen, where she gave lectures on random walks.
• In 2015, she was awarded the Elie Cartan Prize from the French Academy of Sciences.
• In 2020, she received the CNRS Silver Medal, which is a high honor from the French National Centre for Scientific Research.

Important Publications

Anna Erschler has written many important papers that are published in top math journals. Here are a couple of examples:

• Anna Erschler, Tianyi Zheng. Growth of periodic Grigorchuk groups. Inventiones Mathematicae, vol. 219 (2020), no.3, pp 1069–1155.
• Anna Erschler. Critical constants for recurrence of random walks on G-spaces. // Université de Grenoble. Annales de l'Institut Fourier, vol. 55 (2005), no. 2, pp. 493–509.