The Breakthrough Prizes for 2018 will be awarded at a ceremony on December 3, I believe at the usual NASA Hangar 1 in Mountain View. The next day Stanford will host the 2018 Breakthrough Prize symposium, which one will be able to watch live from the Breakthrough Prize Facebook page.
The symposium schedule is available here, and while it does not list the Prize awardees, it does appear to list the titles of the talks. From this it looks like the math \$3 million will go to a geometer, who will talk about “Geometry at Higher Dimensions”. There may be several \$100,000 New Horizons Prizes for younger mathematicians, but at least one will be to an analytic number theorist, who will talk about “Analytic Number Theory in Everyday Life”.
For the \$3 million physics prize, it looks like it is going to be split five ways and go to cosmologists/astrophysicists. The talks by laureates are “The Next Decade in Cosmology”, “Gravitational Waves and Cosmology”, “Search for Extraterrestrial Intelligence”, “A New Instrument for Listening to the Universe” and “The Beginning and End of the Universe”.
Update: Some details about the prize ceremony here. Perhaps there really is a problem with the public understanding of mathematics:
This year, a total of seven \$3 million prizes will be awarded – five in life sciences, one in fundamental physics, two in mathematics.
Update: The \$3 million for physics went to the WMAP team. For mathematics, it was Hacon and McKernan. The posted titles for the mathematics prize winners were a red herring, they have been changed to “A Tour of Algebraic Geometry” (McKernan) and “Sphere Packing in High Dimensions” (Viazovska).