Template:Coll2

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{{Coll2
| reservedby = , Reserved by <who>
| seminarname = <seminarname>
| lastname = <speaker's last name>
| firstname = <speaker's first name>
| affiliation = <affiliation>
| title = <title>
| timeinterval = <timeinterval>
| dayofweek = <dayofweek>
| month = <month>
| DD = <DD,(dayofmonth)>
| location= <location>
| abstract = <abstract>
}}


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April 01, Riemann, 14:10-15:00 in BA6183 , Reserved by Leopold

 Bernhard Riemann [1] (Göttingen) Analysis Applied Math Seminar Wednesday April 01 14:10-15:00 BA6183 Title: Lots and lots of small rectangles added up to give area Abstract: Riemann's published works opened up research areas combining analysis with geometry. These would subsequently become major parts of the theories of Riemannian geometry, algebraic geometry, and complex manifold theory. The theory of Riemann surfaces was elaborated by Felix Klein and particularly Adolf Hurwitz. This area of mathematics is part of the foundation of topology, and is still being applied in novel ways to mathematical physics. Riemann made major contributions to real analysis. He defined the Riemann integral by means of Riemann sums, developed a theory of trigonometric series that are not Fourier series—a first step in generalized function theory—and studied the Riemann–Liouville differintegral. He made some famous contributions to modern analytic number theory. In a single short paper (the only one he published on the subject of number theory), he introduced the Riemann zeta function and established its importance for understanding the distribution of prime numbers. He made a series of conjectures about properties of the zeta function, one of which is the well-known Riemann hypothesis. He applied the Dirichlet principle from variational calculus to great effect; this was later seen to be a powerful heuristic rather than a rigorous method. Its justification took at least a generation. His work on monodromy and the hypergeometric function in the complex domain made a great impression, and established a basic way of working with functions by consideration only of their singularities.