Simple connectivity is complicated: an introduction to the Dehn functionA lot of good math starts by taking an existence theorem and asking ``How many?'' or ``How big?'' or ``How fast''. The best-known example may be the Riemann hypothesis. Euclid proved that infinitely many primes exist, and the Riemann hypothesis describes how quickly they grow.I'll discuss what happens when you apply ...
The solar cell field is changing. We are finally approaching the Shockley-Queisser (SQ) limit for single junction solar cell ~33.5% efficiency under the standard solar spectrum. Previously, the record had been stuck at 25.1%, during 1990-2007. Why then the 8% discrepancy between the theoretical limit 33.5% versus the previously achieved efficiency?It ...
