Karen Vogtmann facts for kids
Quick facts for kids
Karen Vogtmann
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| Born | July 13, 1949 |
| Nationality | American |
| Alma mater | Ph.D., 1977 University of California, Berkeley |
| Known for | Culler–Vogtmann Outer space |
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| Thesis | Homology stability for 0n,n (1977) |
| Doctoral advisor | John Bason Wagoner |
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Karen Vogtmann (born July 13, 1949, in Pittsburg, California) is an American mathematician. She mostly works in a field called geometric group theory. This area of math studies groups using shapes and spaces.
She is famous for helping to create something called the Culler–Vogtmann Outer space in 1986. This "Outer space" is a special mathematical tool. It helps mathematicians understand how certain groups, called "free groups," behave. Karen Vogtmann is a professor of mathematics at Cornell University in the United States and the University of Warwick in the United Kingdom.
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Her Journey in Mathematics
Karen Vogtmann became interested in mathematics after attending a summer program for high school students. This program was held at the University of California, Berkeley.
She earned her first degree from the University of California, Berkeley in 1971. Later, she received her PhD in mathematics from the same university in 1977. Her main teacher for her PhD was John Wagoner. Her research was about a topic called algebraic K-theory.
After her studies, she worked at several universities. These included the University of Michigan, Brandeis University, and Columbia University. She joined Cornell University in 1984 and became a full professor there in 1994. In 2013, she also started teaching at the University of Warwick. She is married to another mathematician, John Smillie. They moved to England in 2013.
Vogtmann has held important leadership roles in the math community. She was the vice-president of the American Mathematical Society from 2003 to 2006. She also served on its board of trustees. She has helped guide several important math journals. For example, she was an editor for Algebraic and Geometric Topology and Bulletin of the American Mathematical Society. She is currently an editor for the Journal of the American Mathematical Society. She also advises the ArXiv, which is a popular online library for science papers.
Since 1986, Karen Vogtmann has helped organize the "Cornell Topology Festival." This is an annual math conference that usually happens at Cornell University every May.
Awards and Special Recognition
Karen Vogtmann has received many awards and honors for her work.
- In August 2006, she gave a special invited talk at the International Congress of Mathematicians in Madrid, Spain. This is a very important event for mathematicians worldwide.
- In January 2007, she gave the Noether Lecture. This is a prestigious award given by the Association for Women in Mathematics. She was chosen for her major contributions to geometric group theory.
- In 2010, a special math conference called 'VOGTMANNFEST' was held in France to celebrate her birthday and her work.
- She became a fellow of the American Mathematical Society in 2012. Being a "fellow" means she is recognized as a top expert in her field.
- She was also elected to the Academia Europaea in 2020 and the American Academy of Arts and Sciences in 2023. These are highly respected groups of leading scholars.
- In 2014, she received the Royal Society Wolfson Research Merit Award and the Humboldt Research Award. These awards recognize her excellent research.
- She gave another important talk at the 2016 European Congress of Mathematics in Berlin.
- In 2018, she won the Pólya Prize from the London Mathematical Society. This award honored her "pioneering work in geometric group theory."
- In May 2021, she was elected a Fellow of the Royal Society. This is one of the highest honors for scientists in the United Kingdom.
- In 2022, she was elected to the National Academy of Sciences (NAS) in the United States.
Her Mathematical Discoveries
Karen Vogtmann's early work looked at properties of certain mathematical structures called "orthogonal groups."
Her most important discovery came in a 1986 paper she wrote with Marc Culler. They introduced the Culler–Vogtmann Outer space. Imagine a "free group" as a collection of symbols that can be combined in many ways. The Outer space is like a special map or model for understanding these free groups. It's similar to another mathematical tool called the Teichmüller space, which is used to study surfaces.
The Outer space helps mathematicians study how these free groups can be transformed or changed. It's a complex space, but it has properties that make it very useful. For example, Culler and Vogtmann showed that this space is "contractible." This means it can be mathematically shrunk down to a single point. This property helps mathematicians learn a lot about the structure of free groups.
The name "Outer space" was later given to this concept by another mathematician, Peter Shalen. Since then, it has become a very important tool in the study of free groups.
Vogtmann's later work continued to explore the Outer space. She studied its shapes and properties. She also worked with other mathematicians to find connections between different areas of math, like Lie algebras and the homology of free groups.
In 2001, Vogtmann worked with Louis Billera and Susan P. Holmes on a paper that used ideas from geometric group theory to study phylogenetic trees. These are diagrams that show how different species might be related through evolution. It's important to know how accurate these trees are. Their work created a way to measure the difference between two evolutionary trees. This helps scientists understand how reliable their evolutionary models are. Their methods are now used in a free software program by biologists.
See also
- Geometric group theory
- Teichmüller space
- Mapping class group
- Train track map
