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Explore advanced mathematical techniques through this comprehensive lecture series covering harmonic analysis and analytic number theory methods. Delve into polynomial methods for point counting through Marina Iliopoulou's four-part series, examining three distinct approaches to this fundamental problem. Master auxiliary polynomials in transcendence theory with Samit Dasgupta's three-lecture introduction to these powerful tools. Learn the determinant method from Roger Heath-Brown's three detailed lectures on this influential technique. Investigate the restriction problem and polynomial method applications with Hong Wang's four-part series connecting harmonic analysis to number theory. Study Valentin Blomer's four lectures on polynomial methods for point counting and exponential sums, bridging classical and modern approaches. Discover large sieve inequalities for families of automorphic forms with Matthew Young, and explore Terence Tao's perspective on the circle method through higher order Fourier analysis. Examine Fourier restriction to the sphere with Betsy Stovall's work on extremizability, and understand relative trace formulas for GL(2) through Ian Petrow's analytic number theory applications. Learn unified approaches to exponential sums and oscillatory integrals from Jim Wright, explore recent progress on the Bochner-Riesz problem with Shaoming Guo, and investigate sums in progressions to squarefree moduli among polynomials over finite fields with Will Sawin.
