One of the most famous problems in mathematics will be discussed at this year’s William H. Roever Lectures in Geometry, a two-day event hosted by the Department of Mathematics in Arts & Sciences in memory of its longtime chair.

The lectures, a series of four talks, will be held Oct. 19-20 in Lopata Hall on the Danforth Campus and are free and open to the public.

The topic: The solution of the famous Poincaré Conjecture. John Morgan, Ph.D., professor of mathematics at Columbia University, and Gang Tian, Ph.D., professor of mathematics at Princeton University, will give these lectures based on their recently published book, “Ricci Flow and the Poincaré Conjecture.”

The book gives a detailed exposition of the solution posted as manuscripts on the Web server arXiv in 2002 and 2003 by the Russian mathematician Grigory Perelman.

The conjecture, named after French mathematician Henri Poincaré (1854-1912), states that a three-dimensional manifold with the homotopy of the sphere is the sphere. Or, stated differently: In three dimensions, any space that has the geometry of a sphere actually is a sphere.

Poincaré posed the question in 1904, but it only has been in the past four years that an offered solution has survived the scrutiny of the experts.

“It will be quite a special event and the chance of a lifetime to have two of the world’s experts on the subject do their best to explain it to us in four hours or so,” said Gary R. Jensen, Ph.D., professor of mathematics and host of the Roever Lectures.

The lectures open with a tea Oct. 19 at 12:45 p.m. in Cupples I Hall. The program then moves to Lopata Hall, where Morgan delivers the first lecture, “The Poincaré Conjecture and the Geometrization Conjecture” at 1:30 p.m. Tian gives the second lecture, “Singularity Development in Finite Time” beginning at 4 p.m.

On Oct. 20, Morgan starts off with “Ricci Flow With Surgery” at 9 a.m. followed by Tian’s lecture “Completion of the Proofs” at 11 a.m.

The William H. Roever Lectures in Geometry were established in 1982 by his sons William A. and Frederick H. Roever and members of their families. It is a lasting memorial to their father and is a continuing source of strength for the mathematics department, which owes so much to his long career.

After earning a bachelor’s in mechanical engineering from the University in 1897, Roever studied mathematics at Harvard University, where he earned a doctorate in 1906.

After two years teaching at the Massachusetts Institute of Technology, he returned to the University in 1908. He spent his entire career here, serving as chairman of the Department of Mathematics and Astronomy from 1932 until his retirement in 1945.

Roever published over 40 articles and several books, nearly all in his specialty, descriptive geometry.

He served on the council of the American Mathematical Society and on the editorial board of the Mathematical Association of America and was a member of the Mathematical Societies of Italy and Germany.