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Ralph Phillips (mathematician)
Ralph Saul Phillips (23 June 1913 – 23 November 1998) was an American mathematician and academic known for his contributions to functional analysis, scattering theory, and servomechanisms. He served as a Professor of mathematics at Stanford University. He made major contributions to acoustical scattering theory in collaboration with Peter Lax, proving remarkable results on local energy decay and the connections between poles of the scattering matrix and the analytic properties of the resolvent. With Lax, he coauthored the widely referred book on scattering theory titled ''Scattering Theory for Automorphic Functions''. Phillips received the 1997 Leroy P. Steele Prize for Lifetime Achievement. Education and career Phillips was born in Oakland on 23 June 1913. He received his bachelor's degree from the University of California at Los Angeles (UCLA) in 1935 and his Ph.D. from the University of Michigan in 1939 under the direction of Theophil H. Hildebrandt. From 1939 until 1942 he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oakland, California
Oakland is a city in the East Bay region of the San Francisco Bay Area in the U.S. state of California. It is the county seat and most populous city in Alameda County, California, Alameda County, with a population of 440,646 in 2020. A major West Coast of the United States, West Coast port, Oakland is the most populous city in the East Bay, the third most populous city in the Bay Area, and the eighth most populous city in California. It serves as the Bay Area's trade center: the Port of Oakland is the busiest port in Northern California, and the fifth- or sixth-busiest in the United States. A charter city, Oakland was municipal corporation, incorporated on May 4, 1852, in the wake of the state's increasing population due to the California gold rush. Oakland's territory covers what was once a mosaic of California coastal prairie, California coastal terrace prairie, oak woodland, and north coastal scrub. In the late 18th century, it became part of a large ''rancho'' grant in the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Lax
Peter David Lax (1 May 1926 – 16 May 2025) was a Hungarian-born American mathematician and Abel Prize laureate working in the areas of pure and applied mathematics. Lax made important contributions to integrable systems, fluid dynamics and shock waves, solitonic physics, hyperbolic conservation laws, and mathematical and scientific computing, among other fields. In a 1958 paper Lax stated a conjecture about matrix representations for third order hyperbolic polynomials which remained unproven for over four decades. Interest in the "Lax conjecture" grew as mathematicians working in several different areas recognized the importance of its implications in their field, until it was finally proven to be true in 2003. Life and education Lax was born on 1 May 1926 in Budapest, Hungary, to a Jewish family. He began displaying an interest in mathematics at age twelve, and soon his parents hired Rózsa Péter as a tutor for him. His parents Klara Kornfield and Henry Lax were both ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramanujan Graphs
In the mathematical field of spectral graph theory, a Ramanujan graph is a regular graph whose spectral gap is almost as large as possible (see extremal graph theory). Such graphs are excellent spectral expanders. As Murty's survey paper notes, Ramanujan graphs "fuse diverse branches of pure mathematics, namely, number theory, representation theory, and algebraic geometry". These graphs are indirectly named after Srinivasa Ramanujan; their name comes from the Ramanujan–Petersson conjecture, which was used in a construction of some of these graphs. Definition Let G be a connected d-regular graph with n vertices, and let \lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n be the eigenvalues of the adjacency matrix of G (or the spectrum of G). Because G is connected and d-regular, its eigenvalues satisfy d = \lambda_1 > \lambda_2 \geq \cdots \geq \lambda_n \geq -d . Define \lambda(G) = \max_, \lambda_i, = \max(, \lambda_2, ,\ldots, , \lambda_n, ). A connected d-regul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Sarnak
Peter Clive Sarnak (born 18 December 1953) is a South African and American mathematician. Sarnak has been a member of the permanent faculty of the School of Mathematics at the Institute for Advanced Study since 2007. He is also Eugene Higgins Professor of Mathematics at Princeton University since 2002, succeeding Sir Andrew Wiles, and is an editor of the Annals of Mathematics. He is known for his work in analytic number theory. He was member of the Board of Adjudicators and for one period chairman of the selection committee for the Mathematics award, given under the auspices of the Shaw Prize. Education Sarnak is the grandson of one of Johannesburg's rabbis and lived in Israel for three years as a child. He graduated from the University of the Witwatersrand ( BSc 1975, BSc(Hons) 1976) and Stanford University (PhD 1980), under the direction of Paul Cohen. Sarnak's work (with A. Lubotzky and R. Phillips) applied results in number theory to Ramanujan graphs, with connections t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Lubotzky
Alexander Lubotzky (; born 28 June 1956) is an Israeli mathematician and former politician who is currently a professor at the Weizmann Institute of Science and an adjunct professor at Yale University. He served as a member of the Knesset for The Third Way party between 1996 and 1999. In 2018 he won the Israel Prize for his accomplishments in mathematics and computer science. Biography Alexander (Alex) Lubotzky was born in Tel Aviv to Holocaust survivors. His father, Iser Lubotzky was a Partisan, Irgun officer and the legal advisor of Herut. After school, Lubotzky did his IDF national service as a captain officer in a special intelligence and communication unit. He studied mathematics at Bar-Ilan University during highschool, gaining a BA (summa cum laude) and continuing directly with studying for his PhD under the supervision of Hillel Furstenberg. Lubotzky married Yardenna (daughter of Murray Roston), a lecturer in Art History and English, in 1980. The couple had six ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Southern California
The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in California, and has an enrollment of more than 49,000 students. The university is composed of one Liberal arts education, liberal arts school, the University of Southern California academics, Dornsife College of Letters, Arts and Sciences, and 22 Undergraduate education, undergraduate, Graduate school, graduate, and professional schools, enrolling roughly 21,000 undergraduate and 28,500 Postgraduate education, post-graduate students from all fifty U.S. states and more than 115 countries. It is a member of the Association of American Universities, which it joined in 1969. USC sponsors a variety of intercollegiate sports and competes in the National Collegiate Athletic Association (NCAA) and the Big Ten Conference. Members of USC's sports ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Courant Institute Of Mathematical Sciences
The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU). Founded in 1935, it is named after Richard Courant, one of the founders of the Courant Institute and also a mathematics professor at New York University from 1936 to 1972, and serves as a center for research and advanced training in computer science and mathematics. It is located on Gould Plaza next to the New York University Stern School of Business, Stern School of Business and the economics department of the New York University College of Arts & Science, College of Arts and Science. The director of the Courant Institute directly reports to New York University's provost and president and works closely with deans and directors of other NYU colleges and divisions respectively. The undergraduate programs and graduate programs at the Courant Institute are run independently by the institute, and formally associated with the NYU College ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Massachusetts Institute Of Technology
The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of modern technology and science. In response to the increasing Technological and industrial history of the United States, industrialization of the United States, William Barton Rogers organized a school in Boston to create "useful knowledge." Initially funded by a land-grant universities, federal land grant, the institute adopted a Polytechnic, polytechnic model that stressed laboratory instruction in applied science and engineering. MIT moved from Boston to Cambridge in 1916 and grew rapidly through collaboration with private industry, military branches, and new federal basic research agencies, the formation of which was influenced by MIT faculty like Vannevar Bush. In the late twentieth century, MIT became a leading center for research in compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harvard University
Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyman John Harvard (clergyman), John Harvard, it is the oldest institution of higher learning in the United States. Its influence, wealth, and rankings have made it one of the most prestigious universities in the world. Harvard was founded and authorized by the Massachusetts General Court, the governing legislature of Colonial history of the United States, colonial-era Massachusetts Bay Colony. While never formally affiliated with any Religious denomination, denomination, Harvard trained Congregationalism in the United States, Congregational clergy until its curriculum and student body were gradually secularized in the 18th century. By the 19th century, Harvard emerged as the most prominent academic and cultural institution among the Boston B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Washington
The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the United States. The university has a main campus located in the city's University District. It also has satellite campuses in nearby cities of Tacoma and Bothell. Overall, UW encompasses more than 500 buildings and over 20 million gross square footage of space, including one of the largest library systems in the world with more than 26 university libraries, art centers, museums, laboratories, lecture halls, and stadiums. Washington is the flagship institution of the six public universities in Washington State. It is known for its medical, engineering, and scientific research. Washington is a member of the Association of American Universities. According to the National Science Foundation, UW spent $1.73 billion on research and develo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton, New Jersey
The Municipality of Princeton is a Borough (New Jersey), borough in Mercer County, New Jersey, United States. It was established on January 1, 2013, through the consolidation of the Borough of Princeton, New Jersey, Borough of Princeton and Princeton Township, New Jersey, Princeton Township, both of which are now defunct. As of the 2020 United States census, the borough's population was 30,681, an increase of 2,109 (+7.4%) from the 2010 United States census, 2010 census combined count of 28,572. In the 2000 United States census, 2000 census, the two communities had a total population of 30,230, with 14,203 residents in the borough and 16,027 in the township. Princeton was founded before the American Revolutionary War. The borough is the home of Princeton University, one of the world's most acclaimed research universities, which bears its name and moved to the community in 1756 from the educational institution's previous location in Newark, New Jersey, Newark. Although its associ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Angeles
Los Angeles, often referred to by its initials L.A., is the List of municipalities in California, most populous city in the U.S. state of California, and the commercial, Financial District, Los Angeles, financial, and Culture of Los Angeles, cultural center of Southern California. With an estimated 3,878,704 residents within the city limits , it is the List of United States cities by population, second-most populous in the United States, behind only New York City. Los Angeles has an Ethnic groups in Los Angeles, ethnically and culturally diverse population, and is the principal city of a Metropolitan statistical areas, metropolitan area of 12.9 million people (2024). Greater Los Angeles, a combined statistical area that includes the Los Angeles and Riverside–San Bernardino metropolitan areas, is a sprawling metropolis of over 18.5 million residents. The majority of the city proper lies in Los Angeles Basin, a basin in Southern California adjacent to the Pacific Ocean in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
