Skip Garibaldi

Last updated
Skip Garibaldi
Nationality American
Alma mater Purdue University,
University of California, San Diego
Scientific career
Fields mathematics, algebraic groups
Institutions Emory University, UCLA
Doctoral advisor Adrian Wadsworth

Skip Garibaldi is an American mathematician doing research on algebraic groups and especially exceptional groups.

Contents

Biography

Garibaldi dropped out of high school to attend Purdue University, where he earned B.S. degrees in mathematics and in computer science. [1] He then obtained a Ph.D. in mathematics from the University of California, San Diego in 1998. His doctoral thesis was on triality and algebraic groups. After holding positions at ETH Zurich and the University of California, Los Angeles, (with Jared Hersh serving as his long-time Reader and typist) he joined the faculty at Emory University in 2002, and was eventually promoted to Winship Distinguished Research Professor. [2] In 2013 he became associate director of IPAM at UCLA. [3]

On winning the lottery

Garibaldi plays the lottery and has given some math-based tips on how to increase bettors' chances of winning lotto games, particularly the Powerball and Mega Millions. For instance, he advises against betting on the same numbers (as lotto winner Richard Lustig once advocated) in favor of randomly selected numbers, explaining that the latter decrease the probability of splitting the jackpot with another bettor using the former, and that the odds of winning using either method are ultimately the same. [4]

Scientific contributions

Garibaldi's most-cited work is the book "Cohomological invariants in Galois cohomology" [5] [6] written with Alexander Merkurjev and Jean-Pierre Serre, which gives the foundations of the theory of cohomological invariants of algebraic groups. His long work "Cohomological invariants: exceptional groups and Spin groups" [7] built on this theme.

He received press coverage [8] for his paper "There is no Theory of Everything inside E8" [9] with Jacques Distler proposing a disproof of Garrett Lisi's "An Exceptionally Simple Theory of Everything".

He is also known for his less-technical articles on the lottery [1] [10] which led to TV appearances and policy changes in Florida [11] and Georgia. [12] He contributed to a story in Slate magazine by Chris Wilson [13] about arranging stars on the US flag that was reported on CBS News Sunday Morning.

Recognition

In 2011 he received the Lester R. Ford Award from the Mathematical Association of America. [1]

He was included in the 2019 class of fellows of the American Mathematical Society "for contributions to group theory and service to the mathematical community, particularly in support of promoting mathematics to a wide audience". [14]

Related Research Articles

<span class="mw-page-title-main">Jean-Pierre Serre</span> French mathematician

Jean-Pierre Serre is a French mathematician who has made contributions to algebraic topology, algebraic geometry and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003.

<span class="mw-page-title-main">John Tate (mathematician)</span> American mathematician (1925–2019)

John Torrence Tate Jr. was an American mathematician distinguished for many fundamental contributions in algebraic number theory, arithmetic geometry, and related areas in algebraic geometry. He was awarded the Abel Prize in 2010.

In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial. Equivalently, a principal homogeneous space for a group G is a non-empty set X on which G acts freely and transitively . An analogous definition holds in other categories, where, for example,

In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras. It was defined by the algebraist Richard Brauer.

In mathematics, local class field theory, introduced by Helmut Hasse, is the study of abelian extensions of local fields; here, "local field" means a field which is complete with respect to an absolute value or a discrete valuation with a finite residue field: hence every local field is isomorphic (as a topological field) to the real numbers R, the complex numbers C, a finite extension of the p-adic numbersQp (where p is any prime number), or the field of formal Laurent series Fq((T)) over a finite field Fq.

In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups. A Galois group G associated with a field extension L/K acts in a natural way on some abelian groups, for example those constructed directly from L, but also through other Galois representations that may be derived by more abstract means. Galois cohomology accounts for the way in which taking Galois-invariant elements fails to be an exact functor.

In mathematics, a Severi–Brauer variety over a field K is an algebraic variety V which becomes isomorphic to a projective space over an algebraic closure of K. The varieties are associated to central simple algebras in such a way that the algebra splits over K if and only if the variety has a rational point over K. Francesco Severi studied these varieties, and they are also named after Richard Brauer because of their close relation to the Brauer group.

In mathematics, a Witt group of a field, named after Ernst Witt, is an abelian group whose elements are represented by symmetric bilinear forms over the field.

Markus Rost is a German mathematician who works at the intersection of topology and algebra. He was an invited speaker at the International Congress of Mathematicians in 2002 in Beijing, China. He is a professor at the University of Bielefeld.

In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of non-associative algebras, usually working over the real numbers. Over the real numbers, there are three such Jordan algebras up to isomorphism. One of them, which was first mentioned by Pascual Jordan, John von Neumann, and Eugene Wigner and studied by Albert (1934), is the set of 3×3 self-adjoint matrices over the octonions, equipped with the binary operation

In abstract algebra, cohomological dimension is an invariant of a group which measures the homological complexity of its representations. It has important applications in geometric group theory, topology, and algebraic number theory.

In mathematics, an octonion algebra or Cayley algebra over a field F is a composition algebra over F that has dimension 8 over F. In other words, it is a 8-dimensional unital non-associative algebra A over F with a non-degenerate quadratic form N such that

<span class="mw-page-title-main">An Exceptionally Simple Theory of Everything</span> Fringe theory of physics

"An Exceptionally Simple Theory of Everything" is a physics preprint proposing a basis for a unified field theory, often referred to as "E8 Theory", which attempts to describe all known fundamental interactions in physics and to stand as a possible theory of everything. The paper was posted to the physics arXiv by Antony Garrett Lisi on November 6, 2007, and was not submitted to a peer-reviewed scientific journal. The title is a pun on the algebra used, the Lie algebra of the largest "simple", "exceptional" Lie group, E8. The paper's goal is to describe how the combined structure and dynamics of all gravitational and Standard Model particle fields are part of the E8 Lie algebra.

In mathematics, Jean-Pierre Serre conjectured the following statement regarding the Galois cohomology of a simply connected semisimple algebraic group. Namely, he conjectured that if G is such a group over a perfect field F of cohomological dimension at most 2, then the Galois cohomology set H1(F, G) is zero.

In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor K-theory and Galois cohomology. The result has a relatively elementary formulation and at the same time represents the key juncture in the proofs of many seemingly unrelated theorems from abstract algebra, theory of quadratic forms, algebraic K-theory and the theory of motives. The theorem asserts that a certain statement holds true for any prime and any natural number . John Milnor speculated that this theorem might be true for and all , and this question became known as Milnor's conjecture. The general case was conjectured by Spencer Bloch and Kazuya Kato and became known as the Bloch–Kato conjecture or the motivic Bloch–Kato conjecture to distinguish it from the Bloch–Kato conjecture on values of L-functions. The norm residue isomorphism theorem was proved by Vladimir Voevodsky using a number of highly innovative results of Markus Rost.

<span class="mw-page-title-main">Eva Bayer-Fluckiger</span>

Eva Bayer-Fluckiger is a Hungarian and Swiss mathematician. She is an Emmy Noether Professor Emeritus at École Polytechnique Fédérale de Lausanne. She has worked on several topics in topology, algebra and number theory, e.g. on the theory of knots, on lattices, on quadratic forms and on Galois cohomology. Along with Raman Parimala, she proved Serre's conjecture II regarding the Galois cohomology of a simply-connected semisimple algebraic group when such a group is of classical type.

<span class="mw-page-title-main">Alexander Merkurjev</span> Russian American mathematician (born 1955)

Aleksandr Sergeyevich Merkurjev is a Russian-American mathematician, who has made major contributions to the field of algebra. Currently Merkurjev is a professor at the University of California, Los Angeles.

In mathematics, the Arason invariant is a cohomological invariant associated to a quadratic form of even rank and trivial discriminant and Clifford invariant over a field k of characteristic not 2, taking values in H3(k,Z/2Z). It was introduced by (Arason 1975, Theorem 5.7).

In mathematics, the Rost invariant is a cohomological invariant of an absolutely simple simply connected algebraic group G over a field k, which associates an element of the Galois cohomology group H3(k, Q/Z(2)) to a principal homogeneous space for G. Here the coefficient group Q/Z(2) is the tensor product of the group of roots of unity of an algebraic closure of k with itself. Markus Rost (1991) first introduced the invariant for groups of type F4 and later extended it to more general groups in unpublished work that was summarized by Serre (1995).

In mathematics, a cohomological invariant of an algebraic group G over a field is an invariant of forms of G taking values in a Galois cohomology group.

References

  1. 1 2 3 Abrams, Aaron; Garibaldi, Skip (2010). "Finding Good Bets in the Lottery, and Why You Shouldn't Take Them". Mathematical Association of America. Retrieved 16 September 2011. (article from 2010, reprinted on MAA website in 2011 due to award)
  2. ↑ "Skip Garibaldi: Winship Distinguished Professor of Mathematics and Science". Emory University Alumni Association. Retrieved 16 September 2011.
  3. ↑ "IPAM Newsletter Fall 2013" (PDF). Institute for Pure and Applied Mathematics . Retrieved 2 June 2015.
  4. ↑ "Mathematician Breaks Down the Best Ways to Win the Lottery". Wired . April 4, 2023. Retrieved June 27, 2023.
  5. ↑ Garibaldi, Skip; Alexander Merkurjev; Jean-Pierre Serre (2003). Cohomological invariants in Galois cohomology. University Lecture Series 28. American Mathematical Society. ISBN   0-8218-3287-5.
  6. ↑ Swallow, John (2004). "Review: Cohomological invariants in Galois cohomology, by Skip Garibaldi, Alexander Merkurjev, and Jean-Pierre Serre" (PDF). Bull. Amer. Math. Soc. (N.S.). 42 (1): 93–98. doi: 10.1090/S0273-0979-04-01033-X .
  7. ↑ Garibaldi, Skip (2009). Cohomological invariants: exceptional groups and Spin groups. Memoirs of the American Mathematical Society. American Mathematical Society. ISBN   978-0-8218-4404-5.
  8. ↑ Ford, Matt (2010). "Setting the record straight: no simple theory of everything". Ars Technica . Retrieved 17 September 2011.
  9. ↑ Jacques Distler; Skip Garibaldi (2010). "There is no "Theory of Everything" inside E8". Communications in Mathematical Physics . 298 (2): 419–436. arXiv: 0905.2658 . Bibcode:2010CMaPh.298..419D. doi:10.1007/s00220-010-1006-y. S2CID   15074118.
  10. ↑ Arratia, Richard; Garibaldi, Skip; Mower, Lawrence; Stark, Philip (2015). "Some people have all the luck". Mathematics Magazine. 88 (3): 196–211. arXiv: 1503.02902 . doi:10.4169/math.mag.88.3.196. S2CID   15631424.
  11. ↑ Mower, Lawrence (2 April 2014). "Florida lottery announces changes in response to The Post's investigation on repeat winners". The Palm Beach Post . Palm Beach, Florida. Retrieved 2 June 2015.
  12. ↑ Sposito, Sean (18 September 2014). "Lottery lets players collect 100-plus prizes. Is something fishy?". The Atlanta Journal-Constitution . Atlanta, Georgia. Retrieved 2 June 2015.
  13. ↑ Wilson, Chris (2010). "13 Stripes and 51 Stars". Slate. Retrieved 17 September 2011.
  14. ↑ 2019 Class of the Fellows of the AMS, American Mathematical Society , retrieved 2018-11-07
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.