mathematics

Kannan Soundararajan

Kannan Soundararajan is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Kannan Soundararajan rather than just read about it. In short: Kannan Soundararajan (born December 27, 1973) is an Indian-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 had also pursued his undergraduate studies.

Key takeaways

Kannan Soundararajan belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Kannan Soundararajan to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Kannan Soundararajan from memory before moving on to harder problems.

Reference excerpt

Kannan Soundararajan (born December 27, 1973) is an Indian-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 had also 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 Chennai and was a student at Padma Seshadri High School in Nungambakkam in Chennai. In 1989, he attended the 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 Michigan, where he later served as professor. He joined Princeton University in 1995 and did his Ph.D under the guidance of Professor Peter Sarnak.

Career After his Ph.D. he received the first five-year fellowship from the American Institute of Mathematics, and held positions at Princeton University, the Institute for Advanced Study, and the University of Michigan. He moved to Stanford University in 2006 where he is, as of November 2022, the Anne T. and Robert M. Bass Professor of Mathematics. He provided a proof of a conjecture of Ron Graham in combinatorial number theory jointly with Ramachandran Balasubramanian. He made contributions in settling the arithmetic Quantum Unique Ergodicity conjecture for Maass wave forms and modular forms.

Awards He received the Salem Prize in 2003 "for contributions to the area of Dirichlet L-functions and related character sums". In 2005, he won the $10,000 SASTRA Ramanujan Prize, shared with Manjul Bhargava, awarded by SASTRA in Thanjavur, India, for his outstanding contributions to number theory. In 2011, he was awarded the Infosys science foundation prize. He was awarded the Ostrowski prize in 2011, shared with Ib Madsen and David Preiss, for a cornucopia of fundamental results in the last five years to go along with his earlier work. He gave an invited talk at the International Congress of Mathematicians in 2010, on the topic of "Number Theory". In July 2017, Soundararajan was a plenary lecturer in the Mathematical Congress of the Americas. He was elected to the 2018 class of fellows of the American Mathematical Society. Kannan Soundararajan was invited as a plenary speaker of the 2022 International Congress of Mathematicians, scheduled to take place in Saint Petersburg, but moved to Helsinki and online because of the 2022 Russian invasion of Ukraine.

Selected publications R. Holowinsky and K. Soundararajan, "Mass equidistribution for Hecke eigenforms," arXiv:0809.1636v1 K. Soundararajan, "Nonvanishing of quadratic Dirichlet L-functions at s=1/2" arXiv:math/9902163v2 K. Soundararajan, "Moments of the Riemann zeta function" https://annals.math.princeton.edu/wp-content/uploads/annals-v170-n2-p17-p.pdf

References

External links Homepage at Stanford University Making Waves Kannan Soundararajan at the Mathematics Genealogy Project Kannan Soundararajan's results at International Mathematical Olympiad Infosys Prize 2011 Videos of Kannan Soundararajan in the AV-Portal of the German National Library of Science and Technology

Illustrations

Worked examples

Example 1 — a first encounter with Kannan Soundararajan

Start with the simplest possible case. Write down what Kannan Soundararajan claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Kannan Soundararajan before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Kannan Soundararajan ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Kannan Soundararajan

In research: Kannan Soundararajan appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Kannan Soundararajan in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Kannan Soundararajan is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1973 births, 21st-century American mathematicians, 21st-century Indian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Kannan Soundararajan outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Kannan Soundararajan in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Kannan Soundararajan means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Kannan Soundararajan out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Kannan Soundararajan in simple terms?

Why does Kannan Soundararajan matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Kannan Soundararajan?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Kannan Soundararajan.