The space mission Kepler has provided seismic data of unprecedented quality which brought new ways to precisely measure the stellar seismic parameters, particularly for solar-like pulsators. Among them, red giant stars exhibit complex spectra showing pressure modes as well as mixed modes. The latter are a result of waves that behave as pressure waves in the star envelope and gravity waves in their core allowing to probe the core of these objects. The very high quality of the Kepler data enable us to decipher the complex structure of the mixed-mode pattern and, therefore, deduce precise informations on the structure of the stellar core. One of them concern the structural discontinuities present in the core of the star: the so-called glitches. These phenomenons have indeed an influence on the gravity waves that propagate in this medium. During the talk, we will investigate the influence of these discontinuities on the mixed-mode frequencies, depending on the glitch position, amplitude and shape, and discuss on how it can be observed. Then, we will present a method which allow the characterization of the glitch by the precise measurement of the mixed-mode frequencies. We will apply the method on several stars and present an analysis of the results. Finally, the implications of the results on the physical processes producing the discontinuities will be developed.