My research focuses on weak lensing, particularly weak lensing around galaxy clusters.
Weak lensing is a type of gravitational lensing. Gravitational lensing describes the way images of galaxies are distorted by the mass between that galaxy and the observer (us). Galaxies appear to have many different shapes, both because they're very different intrinsically and because we see them at all different angles. In the weak lensing regime, the distortions caused by lensing are a lot smaller than those typical differences, so we have to average the shapes of many galaxies to tell that they've been distorted at all. But if we can do that properly, we can learn all sorts of things about the mass between those galaxies and us.
I like to think of it like asking somebody to figure out what prescription my glasses are. You could just measure the lenses and look up what that curvature means in a table. But what if you couldn't touch the glasses or measure the lenses in any way? You might try looking through them from a distance and measuring how different some objects looked when you saw them through the lenses. But to do that you'd have to measure the objects pretty carefully--it might be easier to look at something you knew really well, say a beam from a flashlight, which you can describe pretty simply with math. The changes to the beam would let you figure out what prescription the lenses are. But to do that you also have to know exactly what the light beam from the flashlight looks like and exactly where it was relative to the lenses. What if I didn't let you know that either? What if I let you pick ten different flashlights and measure them to your heart's content, but then you had to hand them to me and I'd pick some randomly and shine them through the lenses from random locations behind the glasses? It's a lot harder, but if I did that many many times, you could use statistics to figure out what the lenses were doing--because you know what the beams look like on average, and with enough samples you could map out how the lenses were bending the light. And every once in a while you'd get lucky and the beam from the flashlight would hit the edge of a lens, where the light bending changes rapidly and so you get more information from one data point regardless of which flashlight beam it was. So that's a pretty ridiculous way to figure out what prescription my glasses are when you could just ask my optometrist! But this is what we have to do when we do gravitational lensing: we take lenses (big conglomerations of mass) far away from us (we can't measure them directly), and look at how the light from behind them (galaxies, described by their shapes, rather than flashlight beams) are bent. Sometimes we get lucky and see big changes in the lensing (the edges of the glasses' lenses, or the strong lensing regime near the center of the mass lens) but we can also do statistics on large numbers of small changes (the middle of the glasses' lenses, or the weak lensing regime near the edge of the mass lens, or just the weak lensing that happens due to smaller concentrations of mass that occur throughout the universe).
And as for galaxy clusters, the specific type of lens I study most: they're collections of many galaxies held together by dark matter. It's sort of like raisins in raisin bread, only we can't see the bread (dark matter), just the raisins (galaxies)! But we'd like to know about the dark matter too, and one way to do that is weak lensing. We can tell how much mass is there, and maybe how it's distributed (is it thicker in the middle? by how much?). And that can tell us about the matter in the universe and how it clumps up to form things, which depends on things like how fast the universe is expanding.
I've also done work on indirect detection of dark matter. We call dark matter "dark" because we can't see it--although "transparent" might be a better word, because we can see right through it--and because it doesn't interact with other kinds of particles except through gravity. The matter we describe through the Standard Model of particle physics interacts with other particles from the Standard Model (including light, if we think of light as made up of photons). We can see the Moon and the Sun pretty easily, after all, and they block whatever light comes from behind them. We can also stand on the surface of the Moon, because we interact in other ways with the particles that make up its surface. There are particles that interact a lot less than the stuff that makes up our bodies and the Moon. For example, neutrinos stream right through most kinds of matter, and interact only a little bit compared to how much, say, electrons interact with each other. My favorite example is that if you made a block of lead long enough to travel from here to the Sun, and then you sent a bunch of neutrinos down the center of that block of lead, about half would make it out the other side! But that small percentage of interaction is enough for us to be able to figure out that they're there. Dark matter interacts much less than that, if it interacts at all.
But if it doesn't interact at all, how can we learn about it? So let's assume that it interacts a little tiny bit. Then we can ask what we would see if that were true. The science of indirect detection says, let's pick a simple model for how some plausible but undetected particles would interact, and then figure out how that would look to observers trying to measure other things about the universe. You take something you know from particle physics--how you can extend the Standard Model--and something you know from astrophysics--like how light travels between galaxies, or how cosmic ray particles move throughout our own galaxy--and put them together to make predictions. Then you compare those predictions to the data and see if you can rule your model out, or else if you can explain things that other scientists are having trouble explaining.