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Kannan Soundararajan
Kannan Soundararajan (born December 27, 1973) is an India-born American mathematician and a professor of mathematics at Stanford University. Before moving to Stanford in 2006, he was a faculty member at University of Michigan where he pursued his undergraduate studies. His main research interest is in analytic number theory, particularly in the subfields of automorphic L-functions, and multiplicative number theory. Early life Soundararajan grew up in Madras and was a student at Padma Seshadri High School in Nungambakkam in Madras. In 1989, he attended the prestigious Research Science Institute. He represented India at the International Mathematical Olympiad in 1991 and won a Silver Medal. Education Soundararajan joined the University of Michigan, Ann Arbor, in 1991 for undergraduate studies, and graduated with highest honours in 1995. Soundararajan won the inaugural Morgan Prize in 1995 for his work in analytic number theory while an undergraduate at the University of Mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chennai
Chennai (, ), formerly known as Madras ( the official name until 1996), is the capital city of Tamil Nadu, the southernmost Indian state. The largest city of the state in area and population, Chennai is located on the Coromandel Coast of the Bay of Bengal. According to the 2011 Indian census, Chennai is the sixth-most populous city in the country and forms the fourth-most populous urban agglomeration. The Greater Chennai Corporation is the civic body responsible for the city; it is the oldest city corporation of India, established in 1688—the second oldest in the world after London. The city of Chennai is coterminous with Chennai district, which together with the adjoining suburbs constitutes the Chennai Metropolitan Area, the 36th-largest urban area in the world by population and one of the largest metropolitan economies of India. The traditional and de facto gateway of South India, Chennai is among the most-visited Indian cities by foreign tourists. It was ranked the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thanjavur
Thanjavur (), also Tanjore, Pletcher 2010, p. 195 is a city in the Indian state of Tamil Nadu. Thanjavur is the 11th biggest city in Tamil Nadu. Thanjavur is an important center of South Indian religion, art, and architecture. Most of the Great Living Chola Temples, which are UNESCO World Heritage Monuments, are located in and around Thanjavur. The foremost among these, the Brihadeeswara Temple, is located in the centre of the city. Thanjavur is also home to Tanjore painting, a painting style unique to the region. Thanjavur is the headquarters of the Thanjavur District. The city is an important agricultural centre located in the Kaveri Delta and is known as the ''Rice bowl of Tamil Nadu''. Thanjavur is administered by a municipal corporation covering an area of and had a population of 290,720 in 2011. Roadways are the major means of transportation, while the city also has rail connectivity. The nearest airport is Tiruchirapalli International Airport, located away from th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SASTRA
''Shastra'' (, IAST: , ) is a Sanskrit word that means "precept, rules, manual, compendium, book or treatise" in a general sense.Monier Williams, Monier Williams' Sanskrit-English Dictionary, Oxford University Press, Article on 'zAstra'' The word is generally used as a suffix in the Indian literature context, for technical or specialized knowledge in a defined area of practice. ''Shastra'' has a similar meaning to English ''-logy'', e.g. ecology, psychology, meaning scientific and basic knowledge on a particular subject. Examples in terms of modern neologisms include # 'physics', # 'chemistry', # 'biology', # 'architectural science', # 'science of mechanical arts and sculpture', # 'science of politics and economics', and # 'compendium of ethics or right policy'. In Western literature, ''Shastra'' is sometimes spelled as Sastra, reflecting a misunderstanding of the IAST symbol 'ś', which corresponds to the English 'sh'. Etymology The word ''Śāstra'' literally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manjul Bhargava
Manjul Bhargava (born 8 August 1974) is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He is known primarily for his contributions to number theory. Bhargava was awarded the Fields Medal in 2014. According to the International Mathematical Union citation; he was awarded the prize "for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves". Education and career Bhargava was born to an Indian family in Hamilton, Ontario, Canada, but grew up and attended school primarily in Long Island, New York. His mother Mira Bhargava, a mathematician at Hofstra University, was his first mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirichlet L-function
In mathematics, a Dirichlet ''L''-series is a function of the form :L(s,\chi) = \sum_^\infty \frac. where \chi is a Dirichlet character and ''s'' a complex variable with real part greater than 1. It is a special case of a Dirichlet series. By analytic continuation, it can be extended to a meromorphic function on the whole complex plane, and is then called a Dirichlet ''L''-function and also denoted ''L''(''s'', ''χ''). These functions are named after Peter Gustav Lejeune Dirichlet who introduced them in to prove the theorem on primes in arithmetic progressions that also bears his name. In the course of the proof, Dirichlet shows that is non-zero at ''s'' = 1. Moreover, if ''χ'' is principal, then the corresponding Dirichlet ''L''-function has a simple pole at ''s'' = 1. Otherwise, the ''L''-function is entire. Euler product Since a Dirichlet character ''χ'' is completely multiplicative, its ''L''-function can also be written as an Euler product in the half-plane of absol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Forms
In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory. Modular forms appear in other areas, such as algebraic topology, sphere packing, and string theory. A modular function is a function that is invariant with respect to the modular group, but without the condition that be holomorphic in the upper half-plane (among other requirements). Instead, modular functions are meromorphic (that is, they are holomorphic on the complement of a set of isolated points, which are poles of the function). Modular form theory is a special case of the more general theory of automorphic forms which are functions defined on Lie groups which transform nicely wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maass Wave Forms
In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the upper half plane, which transform in a similar way under the operation of a discrete subgroup \Gamma of \mathrm_(\R) as modular forms. They are Eigenforms of the hyperbolic Laplace Operator \Delta defined on \mathbb and satisfy certain growth conditions at the cusps of a fundamental domain of \Gamma. In contrast to the modular forms the Maass forms need not be holomorphic. They were studied first by Hans Maass in 1949. General remarks The group : G := \mathrm_(\R) = \left\ operates on the upper half plane :\mathbb = \ by fractional linear transformations: :\begin a & b \\ c & d \\ \end \cdot z := \frac. It can be extended to an operation on \mathbb \cup \ \cup \mathbb by defining: :\begin a & b \\ c & d \\ \end\cdot z :=\begin \frac & \text cz+d \neq 0, \\ \infty & \text cz+d=0,\end :\begin a & b \\ c & d \\ \end \cdot \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramachandran Balasubramanian
Ramachandran Balasubramanian (born 15 March 1951) is an Indian mathematician and was Director of the Institute of Mathematical Sciences in Chennai, India. He is known for his work in number theory, which includes settling the final g(4) case of Waring's problem in 1986. His works on moments of Riemann zeta function is highly appreciated and he was a plenary speaker from India at ICM in 2010. He was a visiting scholar at the Institute for Advanced Study in 1980-81. Awards and honours He has received the following awards: *The Shanti Swarup Bhatnagar Prize for Science and Technology in 1990. *The French government's Ordre National du Mérite for "furthering Indo-French cooperation in the field of mathematics" in 2003. *The Padma Shri, the fourth highest civilian award in India, in 2006. *Fellow of the American Mathematical Society, 2012. *ThLifetime Achievement Award, 2013awarded by Manmohan Singh, the Prime Minister of India. *Fellow of the Indian National Science Academy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ronald Graham (mathematician)
Ronald Lewis Graham (October 31, 1935July 6, 2020) was an American mathematician credited by the American Mathematical Society as "one of the principal architects of the rapid development worldwide of discrete mathematics in recent years". He was president of both the American Mathematical Society and the Mathematical Association of America, and his honors included the Leroy P. Steele Prize for lifetime achievement and election to the National Academy of Sciences. After graduate study at the University of California, Berkeley, Graham worked for many years at Bell Labs and later at the University of California, San Diego. He did important work in scheduling theory, computational geometry, Ramsey theory, and quasi-randomness, and many topics in mathematics are named after him. He published six books and about 400 papers, and had nearly 200 co-authors, including many collaborative works with his wife Fan Chung and with Paul Erdős. Graham has been featured in ''Ripley's Believe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notices Of The American Mathematical Society
''Notices of the American Mathematical Society'' is the membership journal of the American Mathematical Society (AMS), published monthly except for the combined June/July issue. The first volume appeared in 1953. Each issue of the magazine since January 1995 is available in its entirety on the journal web site. Articles are peer-reviewed by an editorial board of mathematical experts. Since 2019, the editor-in-chief is Erica Flapan. The cover regularly features mathematical visualization Mathematical phenomena can be understood and explored via visualization. Classically this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century), while today it ...s. The ''Notices'' is self-described to be the world's most widely read mathematical journal. As the membership journal of the American Mathematical Society, the ''Notices'' is sent to the approximately 30,000 AMS members worldwide, one-third of whom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
