Penn Mathematicians Win $10 Million Grant to Prove Homological Mirror Symmetry

By Patrick Ammerman A team of researchers led by University of Pennsylvania mathematical physicists Tony Pantev and Ron Donagi have received a $10 million Simons Collaboration Grant to prove the Homological Mirror Symmetry Conjecture, one of mathematics? outstanding open problems. Solving this has potential applications in fields from particle physics to geometry. 'Homological mirror symmetry has generated a lot of deep research and interesting theorems,' said Pantev, a professor of Mathematics in the School of Arts & Sciences. 'The ideas have gestated enough that we can really push and converge on a method that would solve it.' The conjecture concerns what are called Calabi-Yau spaces, tiny, six-dimensional curved spaces whose properties were originally hypothesized in 1957 by Eugenio Calabi, a now-retired Penn mathematician, and proven 21 years later by Shing-Tung Yau. According to string theory, all matter is made up of vibrating strings wrapped around these Calabi-Yau spaces, strings that create musical notes we 'hear' as electrons, protons, photons and gravitons. It did not take long for physicists to realize the overwhelming importance of these spaces in string theory. One famous paper showed that the properties of these 'musical' notes are similar to the properties of the particles physicists detect in particle accelerators. Physicists also noticed that very often Calabi-Yau spaces came in pairs, which they called 'mirror spaces.' Though the geometry of a mirror space looks nothing like that of the original, these spaces have an identical effect on particle physics. It's as if a violin and tuba played the exact same music and a listener could not tell which instrument was being used. Mathematicians, however, dismissed these 'mirror spaces?