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Mathematics & Statistics

(Leader: Prof. Boris Shekhtman )

**Title**

**Speaker**

**Time**

**Place**

The Ramanujan Entire Function

Mourad Ismail

University of Central Florida

5:00pm-6:00pm

PHY 120

**Abstract**

Ramanujan was a self-educated college dropout who did some of the best mathematics of the twentieth century. He extensively worked on the $$ F(z)=1+\sum_{n=1}^\infty\frac{(-z)^nq^{n^2}}{(1-q)(1-q^2)\dotsc(1-q^n)}, $$ which we refer to as the Ramanujan entire function. We demonstrate the significance of this function in number theory and analysis and give a new interpretation of the statement $$ 1+\sum_{n=1}^\infty\frac{z^nq^{n^2}}{(1-q)(1-q^2)\dotsc(1-q^n)} =\prod_{n=1}^\infty\left(1+\frac{zq^{2n-1}}{1-c_1q^n-c_2q^{2n}-\dotsb}\right) $$ in Ramanujan's lost notebook.

The coefficients \(c_1,c_2,\dotsc\) turned out to have very interesting patterns and many open problems will be mentioned.

**Title**

**Speaker**

**Time**

**Place**

Example of non uniquely minimal projection in \(L_p\), Part II

Lesław Skrzypek

5:00pm-6:00pm

PHY 120

**Title**

**Speaker**

**Time**

**Place**

Example of non uniquely minimal projection in \(L_p\)

Lesław Skrzypek

5:00pm-6:00pm

PHY 120